|
1993
|
1 // Matrix manipulations. |
|
458
|
2 /* |
|
|
3 |
|
2847
|
4 Copyright (C) 1996, 1997 John W. Eaton |
|
458
|
5 |
|
|
6 This file is part of Octave. |
|
|
7 |
|
|
8 Octave is free software; you can redistribute it and/or modify it |
|
|
9 under the terms of the GNU General Public License as published by the |
|
|
10 Free Software Foundation; either version 2, or (at your option) any |
|
|
11 later version. |
|
|
12 |
|
|
13 Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
16 for more details. |
|
|
17 |
|
|
18 You should have received a copy of the GNU General Public License |
|
|
19 along with Octave; see the file COPYING. If not, write to the Free |
|
1315
|
20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
458
|
21 |
|
|
22 */ |
|
|
23 |
|
4192
|
24 #if defined (__GNUG__) && defined (USE_PRAGMA_INTERFACE_IMPLEMENTATION) |
|
1296
|
25 #pragma implementation |
|
|
26 #endif |
|
|
27 |
|
458
|
28 #ifdef HAVE_CONFIG_H |
|
1192
|
29 #include <config.h> |
|
458
|
30 #endif |
|
|
31 |
|
1367
|
32 #include <cfloat> |
|
|
33 |
|
3503
|
34 #include <iostream> |
|
1367
|
35 |
|
2317
|
36 #include "byte-swap.h" |
|
2828
|
37 #include "dMatrix.h" |
|
1819
|
38 #include "dbleAEPBAL.h" |
|
458
|
39 #include "dbleDET.h" |
|
1819
|
40 #include "dbleSCHUR.h" |
|
740
|
41 #include "dbleSVD.h" |
|
1847
|
42 #include "f77-fcn.h" |
|
458
|
43 #include "lo-error.h" |
|
2354
|
44 #include "lo-ieee.h" |
|
|
45 #include "lo-mappers.h" |
|
1968
|
46 #include "lo-utils.h" |
|
1367
|
47 #include "mx-base.h" |
|
2828
|
48 #include "mx-m-dm.h" |
|
3176
|
49 #include "mx-dm-m.h" |
|
1367
|
50 #include "mx-inlines.cc" |
|
1650
|
51 #include "oct-cmplx.h" |
|
4153
|
52 #include "quit.h" |
|
458
|
53 |
|
3827
|
54 #ifdef HAVE_FFTW |
|
|
55 #include "oct-fftw.h" |
|
|
56 #endif |
|
|
57 |
|
458
|
58 // Fortran functions we call. |
|
|
59 |
|
|
60 extern "C" |
|
|
61 { |
|
3887
|
62 int F77_FUNC (dgebal, DGEBAL) (const char*, const int&, double*, |
|
3331
|
63 const int&, int&, int&, double*, |
|
|
64 int&, long, long); |
|
|
65 |
|
3887
|
66 int F77_FUNC (dgebak, DGEBAK) (const char*, const char*, const int&, |
|
3331
|
67 const int&, const int&, double*, |
|
|
68 const int&, double*, const int&, |
|
|
69 int&, long, long); |
|
|
70 |
|
3887
|
71 int F77_FUNC (dgemm, DGEMM) (const char*, const char*, const int&, |
|
1253
|
72 const int&, const int&, const double&, |
|
|
73 const double*, const int&, |
|
|
74 const double*, const int&, |
|
|
75 const double&, double*, const int&, |
|
|
76 long, long); |
|
458
|
77 |
|
4329
|
78 int F77_FUNC (dgetrf, DGETRF) (const int&, const int&, double*, const int&, |
|
|
79 int*, int&); |
|
|
80 |
|
|
81 int F77_FUNC (dgetrs, DGETRS) (const char*, const int&, const int&, |
|
|
82 const double*, const int&, |
|
|
83 const int*, double*, const int&, int&); |
|
|
84 |
|
|
85 int F77_FUNC (dgetri, DGETRI) (const int&, double*, const int&, const int*, |
|
|
86 double*, const int&, int&); |
|
|
87 |
|
|
88 int F77_FUNC (dgecon, DGECON) (const char*, const int&, double*, |
|
|
89 const int&, const double&, double&, |
|
|
90 double*, int*, int&); |
|
458
|
91 |
|
3887
|
92 int F77_FUNC (dgelss, DGELSS) (const int&, const int&, const int&, |
|
1253
|
93 double*, const int&, double*, |
|
|
94 const int&, double*, double&, int&, |
|
|
95 double*, const int&, int&); |
|
458
|
96 |
|
1360
|
97 // Note that the original complex fft routines were not written for |
|
|
98 // double complex arguments. They have been modified by adding an |
|
|
99 // implicit double precision (a-h,o-z) statement at the beginning of |
|
|
100 // each subroutine. |
|
458
|
101 |
|
3887
|
102 int F77_FUNC (cffti, CFFTI) (const int&, Complex*); |
|
|
103 |
|
|
104 int F77_FUNC (cfftf, CFFTF) (const int&, Complex*, Complex*); |
|
|
105 |
|
|
106 int F77_FUNC (cfftb, CFFTB) (const int&, Complex*, Complex*); |
|
|
107 |
|
|
108 int F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, |
|
1819
|
109 double&, double&); |
|
|
110 |
|
3887
|
111 int F77_FUNC (dtrsyl, DTRSYL) (const char*, const char*, const int&, |
|
1819
|
112 const int&, const int&, const double*, |
|
|
113 const int&, const double*, const int&, |
|
|
114 const double*, const int&, double&, |
|
|
115 int&, long, long); |
|
|
116 |
|
3887
|
117 int F77_FUNC (xdlange, XDLANGE) (const char*, const int&, |
|
3130
|
118 const int&, const double*, |
|
|
119 const int&, double*, double&); |
|
458
|
120 } |
|
|
121 |
|
1360
|
122 // Matrix class. |
|
458
|
123 |
|
2349
|
124 Matrix::Matrix (const RowVector& rv) |
|
|
125 : MArray2<double> (1, rv.length (), 0.0) |
|
|
126 { |
|
|
127 for (int i = 0; i < rv.length (); i++) |
|
|
128 elem (0, i) = rv.elem (i); |
|
|
129 } |
|
|
130 |
|
|
131 Matrix::Matrix (const ColumnVector& cv) |
|
|
132 : MArray2<double> (cv.length (), 1, 0.0) |
|
|
133 { |
|
|
134 for (int i = 0; i < cv.length (); i++) |
|
|
135 elem (i, 0) = cv.elem (i); |
|
|
136 } |
|
|
137 |
|
458
|
138 Matrix::Matrix (const DiagMatrix& a) |
|
1214
|
139 : MArray2<double> (a.rows (), a.cols (), 0.0) |
|
458
|
140 { |
|
|
141 for (int i = 0; i < a.length (); i++) |
|
|
142 elem (i, i) = a.elem (i, i); |
|
|
143 } |
|
|
144 |
|
1574
|
145 // XXX FIXME XXX -- could we use a templated mixed-type copy function |
|
|
146 // here? |
|
|
147 |
|
2828
|
148 Matrix::Matrix (const boolMatrix& a) |
|
|
149 : MArray2<double> (a.rows (), a.cols ()) |
|
|
150 { |
|
|
151 for (int i = 0; i < a.rows (); i++) |
|
|
152 for (int j = 0; j < a.cols (); j++) |
|
|
153 elem (i, j) = a.elem (i, j); |
|
|
154 } |
|
|
155 |
|
1574
|
156 Matrix::Matrix (const charMatrix& a) |
|
|
157 : MArray2<double> (a.rows (), a.cols ()) |
|
|
158 { |
|
|
159 for (int i = 0; i < a.rows (); i++) |
|
|
160 for (int j = 0; j < a.cols (); j++) |
|
|
161 elem (i, j) = a.elem (i, j); |
|
|
162 } |
|
|
163 |
|
2385
|
164 bool |
|
458
|
165 Matrix::operator == (const Matrix& a) const |
|
|
166 { |
|
|
167 if (rows () != a.rows () || cols () != a.cols ()) |
|
2385
|
168 return false; |
|
458
|
169 |
|
3769
|
170 return mx_inline_equal (data (), a.data (), length ()); |
|
458
|
171 } |
|
|
172 |
|
2385
|
173 bool |
|
458
|
174 Matrix::operator != (const Matrix& a) const |
|
|
175 { |
|
|
176 return !(*this == a); |
|
|
177 } |
|
|
178 |
|
3354
|
179 bool |
|
|
180 Matrix::is_symmetric (void) const |
|
|
181 { |
|
|
182 if (is_square () && rows () > 0) |
|
|
183 { |
|
|
184 for (int i = 0; i < rows (); i++) |
|
|
185 for (int j = i+1; j < cols (); j++) |
|
|
186 if (elem (i, j) != elem (j, i)) |
|
|
187 return false; |
|
|
188 |
|
|
189 return true; |
|
|
190 } |
|
|
191 |
|
|
192 return false; |
|
|
193 } |
|
|
194 |
|
458
|
195 Matrix& |
|
|
196 Matrix::insert (const Matrix& a, int r, int c) |
|
|
197 { |
|
1561
|
198 Array2<double>::insert (a, r, c); |
|
458
|
199 return *this; |
|
|
200 } |
|
|
201 |
|
|
202 Matrix& |
|
|
203 Matrix::insert (const RowVector& a, int r, int c) |
|
|
204 { |
|
|
205 int a_len = a.length (); |
|
4316
|
206 |
|
1698
|
207 if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) |
|
458
|
208 { |
|
|
209 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
210 return *this; |
|
|
211 } |
|
|
212 |
|
4316
|
213 if (a_len > 0) |
|
|
214 { |
|
|
215 make_unique (); |
|
|
216 |
|
|
217 for (int i = 0; i < a_len; i++) |
|
|
218 xelem (r, c+i) = a.elem (i); |
|
|
219 } |
|
458
|
220 |
|
|
221 return *this; |
|
|
222 } |
|
|
223 |
|
|
224 Matrix& |
|
|
225 Matrix::insert (const ColumnVector& a, int r, int c) |
|
|
226 { |
|
|
227 int a_len = a.length (); |
|
4316
|
228 |
|
1698
|
229 if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) |
|
458
|
230 { |
|
|
231 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
232 return *this; |
|
|
233 } |
|
|
234 |
|
4316
|
235 if (a_len > 0) |
|
|
236 { |
|
|
237 make_unique (); |
|
|
238 |
|
|
239 for (int i = 0; i < a_len; i++) |
|
|
240 xelem (r+i, c) = a.elem (i); |
|
|
241 } |
|
458
|
242 |
|
|
243 return *this; |
|
|
244 } |
|
|
245 |
|
|
246 Matrix& |
|
|
247 Matrix::insert (const DiagMatrix& a, int r, int c) |
|
|
248 { |
|
1697
|
249 int a_nr = a.rows (); |
|
|
250 int a_nc = a.cols (); |
|
|
251 |
|
1698
|
252 if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) |
|
458
|
253 { |
|
|
254 (*current_liboctave_error_handler) ("range error for insert"); |
|
|
255 return *this; |
|
|
256 } |
|
|
257 |
|
1697
|
258 fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); |
|
|
259 |
|
4316
|
260 int a_len = a.length (); |
|
|
261 |
|
|
262 if (a_len > 0) |
|
|
263 { |
|
|
264 make_unique (); |
|
|
265 |
|
|
266 for (int i = 0; i < a_len; i++) |
|
|
267 xelem (r+i, c+i) = a.elem (i, i); |
|
|
268 } |
|
458
|
269 |
|
|
270 return *this; |
|
|
271 } |
|
|
272 |
|
|
273 Matrix& |
|
|
274 Matrix::fill (double val) |
|
|
275 { |
|
|
276 int nr = rows (); |
|
|
277 int nc = cols (); |
|
4316
|
278 |
|
458
|
279 if (nr > 0 && nc > 0) |
|
4316
|
280 { |
|
|
281 make_unique (); |
|
|
282 |
|
|
283 for (int j = 0; j < nc; j++) |
|
|
284 for (int i = 0; i < nr; i++) |
|
|
285 xelem (i, j) = val; |
|
|
286 } |
|
458
|
287 |
|
|
288 return *this; |
|
|
289 } |
|
|
290 |
|
|
291 Matrix& |
|
|
292 Matrix::fill (double val, int r1, int c1, int r2, int c2) |
|
|
293 { |
|
|
294 int nr = rows (); |
|
|
295 int nc = cols (); |
|
4316
|
296 |
|
458
|
297 if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 |
|
|
298 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) |
|
|
299 { |
|
|
300 (*current_liboctave_error_handler) ("range error for fill"); |
|
|
301 return *this; |
|
|
302 } |
|
|
303 |
|
|
304 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
305 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
306 |
|
4316
|
307 if (r2 >= r1 && c2 >= c1) |
|
|
308 { |
|
|
309 make_unique (); |
|
|
310 |
|
|
311 for (int j = c1; j <= c2; j++) |
|
|
312 for (int i = r1; i <= r2; i++) |
|
|
313 xelem (i, j) = val; |
|
|
314 } |
|
458
|
315 |
|
|
316 return *this; |
|
|
317 } |
|
|
318 |
|
|
319 Matrix |
|
|
320 Matrix::append (const Matrix& a) const |
|
|
321 { |
|
|
322 int nr = rows (); |
|
|
323 int nc = cols (); |
|
|
324 if (nr != a.rows ()) |
|
|
325 { |
|
|
326 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
327 return Matrix (); |
|
|
328 } |
|
|
329 |
|
|
330 int nc_insert = nc; |
|
|
331 Matrix retval (nr, nc + a.cols ()); |
|
|
332 retval.insert (*this, 0, 0); |
|
|
333 retval.insert (a, 0, nc_insert); |
|
|
334 return retval; |
|
|
335 } |
|
|
336 |
|
|
337 Matrix |
|
|
338 Matrix::append (const RowVector& a) const |
|
|
339 { |
|
|
340 int nr = rows (); |
|
|
341 int nc = cols (); |
|
|
342 if (nr != 1) |
|
|
343 { |
|
|
344 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
345 return Matrix (); |
|
|
346 } |
|
|
347 |
|
|
348 int nc_insert = nc; |
|
|
349 Matrix retval (nr, nc + a.length ()); |
|
|
350 retval.insert (*this, 0, 0); |
|
|
351 retval.insert (a, 0, nc_insert); |
|
|
352 return retval; |
|
|
353 } |
|
|
354 |
|
|
355 Matrix |
|
|
356 Matrix::append (const ColumnVector& a) const |
|
|
357 { |
|
|
358 int nr = rows (); |
|
|
359 int nc = cols (); |
|
|
360 if (nr != a.length ()) |
|
|
361 { |
|
|
362 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
363 return Matrix (); |
|
|
364 } |
|
|
365 |
|
|
366 int nc_insert = nc; |
|
|
367 Matrix retval (nr, nc + 1); |
|
|
368 retval.insert (*this, 0, 0); |
|
|
369 retval.insert (a, 0, nc_insert); |
|
|
370 return retval; |
|
|
371 } |
|
|
372 |
|
|
373 Matrix |
|
|
374 Matrix::append (const DiagMatrix& a) const |
|
|
375 { |
|
|
376 int nr = rows (); |
|
|
377 int nc = cols (); |
|
|
378 if (nr != a.rows ()) |
|
|
379 { |
|
|
380 (*current_liboctave_error_handler) ("row dimension mismatch for append"); |
|
|
381 return *this; |
|
|
382 } |
|
|
383 |
|
|
384 int nc_insert = nc; |
|
|
385 Matrix retval (nr, nc + a.cols ()); |
|
|
386 retval.insert (*this, 0, 0); |
|
|
387 retval.insert (a, 0, nc_insert); |
|
|
388 return retval; |
|
|
389 } |
|
|
390 |
|
|
391 Matrix |
|
|
392 Matrix::stack (const Matrix& a) const |
|
|
393 { |
|
|
394 int nr = rows (); |
|
|
395 int nc = cols (); |
|
|
396 if (nc != a.cols ()) |
|
|
397 { |
|
|
398 (*current_liboctave_error_handler) |
|
|
399 ("column dimension mismatch for stack"); |
|
|
400 return Matrix (); |
|
|
401 } |
|
|
402 |
|
|
403 int nr_insert = nr; |
|
|
404 Matrix retval (nr + a.rows (), nc); |
|
|
405 retval.insert (*this, 0, 0); |
|
|
406 retval.insert (a, nr_insert, 0); |
|
|
407 return retval; |
|
|
408 } |
|
|
409 |
|
|
410 Matrix |
|
|
411 Matrix::stack (const RowVector& a) const |
|
|
412 { |
|
|
413 int nr = rows (); |
|
|
414 int nc = cols (); |
|
|
415 if (nc != a.length ()) |
|
|
416 { |
|
|
417 (*current_liboctave_error_handler) |
|
|
418 ("column dimension mismatch for stack"); |
|
|
419 return Matrix (); |
|
|
420 } |
|
|
421 |
|
|
422 int nr_insert = nr; |
|
|
423 Matrix retval (nr + 1, nc); |
|
|
424 retval.insert (*this, 0, 0); |
|
|
425 retval.insert (a, nr_insert, 0); |
|
|
426 return retval; |
|
|
427 } |
|
|
428 |
|
|
429 Matrix |
|
|
430 Matrix::stack (const ColumnVector& a) const |
|
|
431 { |
|
|
432 int nr = rows (); |
|
|
433 int nc = cols (); |
|
|
434 if (nc != 1) |
|
|
435 { |
|
|
436 (*current_liboctave_error_handler) |
|
|
437 ("column dimension mismatch for stack"); |
|
|
438 return Matrix (); |
|
|
439 } |
|
|
440 |
|
|
441 int nr_insert = nr; |
|
|
442 Matrix retval (nr + a.length (), nc); |
|
|
443 retval.insert (*this, 0, 0); |
|
|
444 retval.insert (a, nr_insert, 0); |
|
|
445 return retval; |
|
|
446 } |
|
|
447 |
|
|
448 Matrix |
|
|
449 Matrix::stack (const DiagMatrix& a) const |
|
|
450 { |
|
|
451 int nr = rows (); |
|
|
452 int nc = cols (); |
|
|
453 if (nc != a.cols ()) |
|
|
454 { |
|
|
455 (*current_liboctave_error_handler) |
|
|
456 ("column dimension mismatch for stack"); |
|
|
457 return Matrix (); |
|
|
458 } |
|
|
459 |
|
|
460 int nr_insert = nr; |
|
|
461 Matrix retval (nr + a.rows (), nc); |
|
|
462 retval.insert (*this, 0, 0); |
|
|
463 retval.insert (a, nr_insert, 0); |
|
|
464 return retval; |
|
|
465 } |
|
|
466 |
|
|
467 Matrix |
|
1205
|
468 real (const ComplexMatrix& a) |
|
|
469 { |
|
|
470 int a_len = a.length (); |
|
|
471 Matrix retval; |
|
|
472 if (a_len > 0) |
|
3769
|
473 retval = Matrix (mx_inline_real_dup (a.data (), a_len), |
|
|
474 a.rows (), a.cols ()); |
|
1205
|
475 return retval; |
|
|
476 } |
|
|
477 |
|
|
478 Matrix |
|
|
479 imag (const ComplexMatrix& a) |
|
|
480 { |
|
|
481 int a_len = a.length (); |
|
|
482 Matrix retval; |
|
|
483 if (a_len > 0) |
|
3769
|
484 retval = Matrix (mx_inline_imag_dup (a.data (), a_len), |
|
|
485 a.rows (), a.cols ()); |
|
1205
|
486 return retval; |
|
|
487 } |
|
|
488 |
|
|
489 Matrix |
|
458
|
490 Matrix::extract (int r1, int c1, int r2, int c2) const |
|
|
491 { |
|
|
492 if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; } |
|
|
493 if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; } |
|
|
494 |
|
|
495 int new_r = r2 - r1 + 1; |
|
|
496 int new_c = c2 - c1 + 1; |
|
|
497 |
|
|
498 Matrix result (new_r, new_c); |
|
|
499 |
|
|
500 for (int j = 0; j < new_c; j++) |
|
|
501 for (int i = 0; i < new_r; i++) |
|
4316
|
502 result.xelem (i, j) = elem (r1+i, c1+j); |
|
|
503 |
|
|
504 return result; |
|
|
505 } |
|
|
506 |
|
|
507 Matrix |
|
|
508 Matrix::extract_n (int r1, int c1, int nr, int nc) const |
|
|
509 { |
|
|
510 Matrix result (nr, nc); |
|
|
511 |
|
|
512 for (int j = 0; j < nc; j++) |
|
|
513 for (int i = 0; i < nr; i++) |
|
|
514 result.xelem (i, j) = elem (r1+i, c1+j); |
|
458
|
515 |
|
|
516 return result; |
|
|
517 } |
|
|
518 |
|
|
519 // extract row or column i. |
|
|
520 |
|
|
521 RowVector |
|
|
522 Matrix::row (int i) const |
|
|
523 { |
|
|
524 int nc = cols (); |
|
|
525 if (i < 0 || i >= rows ()) |
|
|
526 { |
|
|
527 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
528 return RowVector (); |
|
|
529 } |
|
|
530 |
|
|
531 RowVector retval (nc); |
|
|
532 for (int j = 0; j < nc; j++) |
|
4316
|
533 retval.xelem (j) = elem (i, j); |
|
458
|
534 |
|
|
535 return retval; |
|
|
536 } |
|
|
537 |
|
|
538 RowVector |
|
|
539 Matrix::row (char *s) const |
|
|
540 { |
|
533
|
541 if (! s) |
|
458
|
542 { |
|
|
543 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
544 return RowVector (); |
|
|
545 } |
|
|
546 |
|
|
547 char c = *s; |
|
|
548 if (c == 'f' || c == 'F') |
|
|
549 return row (0); |
|
|
550 else if (c == 'l' || c == 'L') |
|
|
551 return row (rows () - 1); |
|
|
552 else |
|
|
553 { |
|
|
554 (*current_liboctave_error_handler) ("invalid row selection"); |
|
|
555 return RowVector (); |
|
|
556 } |
|
|
557 } |
|
|
558 |
|
|
559 ColumnVector |
|
|
560 Matrix::column (int i) const |
|
|
561 { |
|
|
562 int nr = rows (); |
|
|
563 if (i < 0 || i >= cols ()) |
|
|
564 { |
|
|
565 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
566 return ColumnVector (); |
|
|
567 } |
|
|
568 |
|
|
569 ColumnVector retval (nr); |
|
|
570 for (int j = 0; j < nr; j++) |
|
4316
|
571 retval.xelem (j) = elem (j, i); |
|
458
|
572 |
|
|
573 return retval; |
|
|
574 } |
|
|
575 |
|
|
576 ColumnVector |
|
|
577 Matrix::column (char *s) const |
|
|
578 { |
|
533
|
579 if (! s) |
|
458
|
580 { |
|
|
581 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
582 return ColumnVector (); |
|
|
583 } |
|
|
584 |
|
|
585 char c = *s; |
|
|
586 if (c == 'f' || c == 'F') |
|
|
587 return column (0); |
|
|
588 else if (c == 'l' || c == 'L') |
|
|
589 return column (cols () - 1); |
|
|
590 else |
|
|
591 { |
|
|
592 (*current_liboctave_error_handler) ("invalid column selection"); |
|
|
593 return ColumnVector (); |
|
|
594 } |
|
|
595 } |
|
|
596 |
|
|
597 Matrix |
|
|
598 Matrix::inverse (void) const |
|
|
599 { |
|
|
600 int info; |
|
|
601 double rcond; |
|
4329
|
602 return inverse (info, rcond, 0, 0); |
|
458
|
603 } |
|
|
604 |
|
|
605 Matrix |
|
|
606 Matrix::inverse (int& info) const |
|
|
607 { |
|
|
608 double rcond; |
|
4329
|
609 return inverse (info, rcond, 0, 0); |
|
458
|
610 } |
|
|
611 |
|
|
612 Matrix |
|
4329
|
613 Matrix::inverse (int& info, double& rcond, int force, int calc_cond) const |
|
458
|
614 { |
|
1948
|
615 Matrix retval; |
|
|
616 |
|
458
|
617 int nr = rows (); |
|
|
618 int nc = cols (); |
|
1948
|
619 |
|
458
|
620 if (nr != nc || nr == 0 || nc == 0) |
|
1948
|
621 (*current_liboctave_error_handler) ("inverse requires square matrix"); |
|
458
|
622 else |
|
|
623 { |
|
1948
|
624 Array<int> ipvt (nr); |
|
|
625 int *pipvt = ipvt.fortran_vec (); |
|
|
626 |
|
|
627 retval = *this; |
|
|
628 double *tmp_data = retval.fortran_vec (); |
|
|
629 |
|
4329
|
630 Array<double> z(1); |
|
|
631 int lwork = -1; |
|
|
632 |
|
|
633 // Query the optimum work array size |
|
|
634 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
635 z.fortran_vec (), lwork, info)); |
|
|
636 |
|
|
637 if (f77_exception_encountered) |
|
|
638 { |
|
|
639 (*current_liboctave_error_handler) |
|
|
640 ("unrecoverable error in dgetri"); |
|
|
641 return retval; |
|
|
642 } |
|
|
643 |
|
|
644 lwork = static_cast<int> (z(0)); |
|
|
645 lwork = (lwork < 2 *nc ? 2*nc : lwork); |
|
|
646 z.resize (lwork); |
|
|
647 double *pz = z.fortran_vec (); |
|
|
648 |
|
|
649 info = 0; |
|
|
650 |
|
|
651 /* Calculate the norm of the matrix, for later use */ |
|
|
652 double anorm = 0; |
|
|
653 if (calc_cond) |
|
|
654 anorm = retval.abs().sum().row(0).max(); |
|
|
655 |
|
|
656 F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); |
|
1948
|
657 |
|
|
658 if (f77_exception_encountered) |
|
4329
|
659 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
660 else |
|
|
661 { |
|
4329
|
662 /* Throw-away extra info LAPACK gives so as to not change output */ |
|
|
663 rcond = 0.; |
|
|
664 if ( info != 0) |
|
1948
|
665 info = -1; |
|
4329
|
666 else if (calc_cond) |
|
|
667 { |
|
|
668 /* Now calculate the condition number for non-singular matrix */ |
|
|
669 char job = '1'; |
|
|
670 Array<int> iz (nc); |
|
|
671 int *piz = iz.fortran_vec (); |
|
|
672 F77_XFCN (dgecon, DGECON, ( &job, nc, tmp_data, nr, anorm, |
|
|
673 rcond, pz, piz, info)); |
|
|
674 |
|
|
675 if (f77_exception_encountered) |
|
|
676 (*current_liboctave_error_handler) |
|
|
677 ("unrecoverable error in dgecon"); |
|
|
678 |
|
|
679 if ( info != 0) |
|
|
680 info = -1; |
|
|
681 } |
|
1948
|
682 |
|
|
683 if (info == -1 && ! force) |
|
|
684 retval = *this; // Restore matrix contents. |
|
|
685 else |
|
|
686 { |
|
4329
|
687 F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, |
|
|
688 pz, lwork, info)); |
|
1948
|
689 |
|
|
690 if (f77_exception_encountered) |
|
|
691 (*current_liboctave_error_handler) |
|
4329
|
692 ("unrecoverable error in dgetri"); |
|
|
693 |
|
|
694 if ( info != 0) |
|
|
695 info = -1; |
|
1948
|
696 } |
|
|
697 } |
|
458
|
698 } |
|
|
699 |
|
1948
|
700 return retval; |
|
458
|
701 } |
|
|
702 |
|
740
|
703 Matrix |
|
|
704 Matrix::pseudo_inverse (double tol) |
|
|
705 { |
|
3480
|
706 SVD result (*this, SVD::economy); |
|
740
|
707 |
|
|
708 DiagMatrix S = result.singular_values (); |
|
|
709 Matrix U = result.left_singular_matrix (); |
|
|
710 Matrix V = result.right_singular_matrix (); |
|
|
711 |
|
|
712 ColumnVector sigma = S.diag (); |
|
|
713 |
|
|
714 int r = sigma.length () - 1; |
|
|
715 int nr = rows (); |
|
|
716 int nc = cols (); |
|
|
717 |
|
|
718 if (tol <= 0.0) |
|
|
719 { |
|
|
720 if (nr > nc) |
|
|
721 tol = nr * sigma.elem (0) * DBL_EPSILON; |
|
|
722 else |
|
|
723 tol = nc * sigma.elem (0) * DBL_EPSILON; |
|
|
724 } |
|
|
725 |
|
|
726 while (r >= 0 && sigma.elem (r) < tol) |
|
|
727 r--; |
|
|
728 |
|
|
729 if (r < 0) |
|
|
730 return Matrix (nc, nr, 0.0); |
|
|
731 else |
|
|
732 { |
|
|
733 Matrix Ur = U.extract (0, 0, nr-1, r); |
|
|
734 DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); |
|
|
735 Matrix Vr = V.extract (0, 0, nc-1, r); |
|
|
736 return Vr * D * Ur.transpose (); |
|
|
737 } |
|
|
738 } |
|
|
739 |
|
3827
|
740 #ifdef HAVE_FFTW |
|
|
741 |
|
|
742 ComplexMatrix |
|
|
743 Matrix::fourier (void) const |
|
|
744 { |
|
|
745 size_t nr = rows (); |
|
|
746 size_t nc = cols (); |
|
|
747 |
|
|
748 ComplexMatrix retval (nr, nc); |
|
|
749 |
|
|
750 size_t npts, nsamples; |
|
|
751 |
|
|
752 if (nr == 1 || nc == 1) |
|
|
753 { |
|
|
754 npts = nr > nc ? nr : nc; |
|
|
755 nsamples = 1; |
|
|
756 } |
|
|
757 else |
|
|
758 { |
|
|
759 npts = nr; |
|
|
760 nsamples = nc; |
|
|
761 } |
|
|
762 |
|
|
763 ComplexMatrix tmp (*this); |
|
|
764 Complex *in (tmp.fortran_vec ()); |
|
|
765 Complex *out (retval.fortran_vec ()); |
|
|
766 |
|
|
767 for (size_t i = 0; i < nsamples; i++) |
|
|
768 { |
|
4153
|
769 OCTAVE_QUIT; |
|
|
770 |
|
3827
|
771 octave_fftw::fft (&in[npts * i], &out[npts * i], npts); |
|
|
772 } |
|
|
773 |
|
|
774 return retval; |
|
|
775 } |
|
|
776 |
|
|
777 ComplexMatrix |
|
|
778 Matrix::ifourier (void) const |
|
|
779 { |
|
|
780 size_t nr = rows (); |
|
|
781 size_t nc = cols (); |
|
|
782 |
|
|
783 ComplexMatrix retval (nr, nc); |
|
|
784 |
|
|
785 size_t npts, nsamples; |
|
|
786 |
|
|
787 if (nr == 1 || nc == 1) |
|
|
788 { |
|
|
789 npts = nr > nc ? nr : nc; |
|
|
790 nsamples = 1; |
|
|
791 } |
|
|
792 else |
|
|
793 { |
|
|
794 npts = nr; |
|
|
795 nsamples = nc; |
|
|
796 } |
|
|
797 |
|
|
798 ComplexMatrix tmp (*this); |
|
|
799 Complex *in (tmp.fortran_vec ()); |
|
|
800 Complex *out (retval.fortran_vec ()); |
|
|
801 |
|
|
802 for (size_t i = 0; i < nsamples; i++) |
|
|
803 { |
|
4153
|
804 OCTAVE_QUIT; |
|
|
805 |
|
3827
|
806 octave_fftw::ifft (&in[npts * i], &out[npts * i], npts); |
|
|
807 } |
|
|
808 |
|
|
809 return retval; |
|
|
810 } |
|
|
811 |
|
|
812 ComplexMatrix |
|
|
813 Matrix::fourier2d (void) const |
|
|
814 { |
|
|
815 int nr = rows (); |
|
|
816 int nc = cols (); |
|
|
817 |
|
|
818 ComplexMatrix retval (*this); |
|
|
819 // Note the order of passing the rows and columns to account for |
|
|
820 // column-major storage. |
|
|
821 octave_fftw::fft2d (retval.fortran_vec (), nc, nr); |
|
|
822 |
|
|
823 return retval; |
|
|
824 } |
|
|
825 |
|
|
826 ComplexMatrix |
|
|
827 Matrix::ifourier2d (void) const |
|
|
828 { |
|
|
829 int nr = rows (); |
|
|
830 int nc = cols (); |
|
|
831 |
|
|
832 ComplexMatrix retval (*this); |
|
|
833 // Note the order of passing the rows and columns to account for |
|
|
834 // column-major storage. |
|
|
835 octave_fftw::ifft2d (retval.fortran_vec (), nc, nr); |
|
|
836 |
|
|
837 return retval; |
|
|
838 } |
|
|
839 |
|
|
840 #else |
|
|
841 |
|
458
|
842 ComplexMatrix |
|
|
843 Matrix::fourier (void) const |
|
|
844 { |
|
1948
|
845 ComplexMatrix retval; |
|
|
846 |
|
458
|
847 int nr = rows (); |
|
|
848 int nc = cols (); |
|
1948
|
849 |
|
458
|
850 int npts, nsamples; |
|
1948
|
851 |
|
458
|
852 if (nr == 1 || nc == 1) |
|
|
853 { |
|
|
854 npts = nr > nc ? nr : nc; |
|
|
855 nsamples = 1; |
|
|
856 } |
|
|
857 else |
|
|
858 { |
|
|
859 npts = nr; |
|
|
860 nsamples = nc; |
|
|
861 } |
|
|
862 |
|
|
863 int nn = 4*npts+15; |
|
1948
|
864 |
|
|
865 Array<Complex> wsave (nn); |
|
|
866 Complex *pwsave = wsave.fortran_vec (); |
|
|
867 |
|
3585
|
868 retval = ComplexMatrix (*this); |
|
1948
|
869 Complex *tmp_data = retval.fortran_vec (); |
|
|
870 |
|
3887
|
871 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
872 |
|
|
873 for (int j = 0; j < nsamples; j++) |
|
4153
|
874 { |
|
|
875 OCTAVE_QUIT; |
|
|
876 |
|
|
877 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
878 } |
|
1948
|
879 |
|
|
880 return retval; |
|
458
|
881 } |
|
|
882 |
|
|
883 ComplexMatrix |
|
|
884 Matrix::ifourier (void) const |
|
|
885 { |
|
1948
|
886 ComplexMatrix retval; |
|
|
887 |
|
458
|
888 int nr = rows (); |
|
|
889 int nc = cols (); |
|
1948
|
890 |
|
458
|
891 int npts, nsamples; |
|
1948
|
892 |
|
458
|
893 if (nr == 1 || nc == 1) |
|
|
894 { |
|
|
895 npts = nr > nc ? nr : nc; |
|
|
896 nsamples = 1; |
|
|
897 } |
|
|
898 else |
|
|
899 { |
|
|
900 npts = nr; |
|
|
901 nsamples = nc; |
|
|
902 } |
|
|
903 |
|
|
904 int nn = 4*npts+15; |
|
1948
|
905 |
|
|
906 Array<Complex> wsave (nn); |
|
|
907 Complex *pwsave = wsave.fortran_vec (); |
|
|
908 |
|
3585
|
909 retval = ComplexMatrix (*this); |
|
1948
|
910 Complex *tmp_data = retval.fortran_vec (); |
|
|
911 |
|
3887
|
912 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
458
|
913 |
|
|
914 for (int j = 0; j < nsamples; j++) |
|
4153
|
915 { |
|
|
916 OCTAVE_QUIT; |
|
|
917 |
|
|
918 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
919 } |
|
458
|
920 |
|
1321
|
921 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
922 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
458
|
923 |
|
1948
|
924 return retval; |
|
458
|
925 } |
|
|
926 |
|
677
|
927 ComplexMatrix |
|
|
928 Matrix::fourier2d (void) const |
|
|
929 { |
|
1948
|
930 ComplexMatrix retval; |
|
|
931 |
|
677
|
932 int nr = rows (); |
|
|
933 int nc = cols (); |
|
1948
|
934 |
|
677
|
935 int npts, nsamples; |
|
1948
|
936 |
|
677
|
937 if (nr == 1 || nc == 1) |
|
|
938 { |
|
|
939 npts = nr > nc ? nr : nc; |
|
|
940 nsamples = 1; |
|
|
941 } |
|
|
942 else |
|
|
943 { |
|
|
944 npts = nr; |
|
|
945 nsamples = nc; |
|
|
946 } |
|
|
947 |
|
|
948 int nn = 4*npts+15; |
|
1948
|
949 |
|
|
950 Array<Complex> wsave (nn); |
|
|
951 Complex *pwsave = wsave.fortran_vec (); |
|
|
952 |
|
3585
|
953 retval = ComplexMatrix (*this); |
|
1948
|
954 Complex *tmp_data = retval.fortran_vec (); |
|
|
955 |
|
3887
|
956 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
957 |
|
|
958 for (int j = 0; j < nsamples; j++) |
|
4153
|
959 { |
|
|
960 OCTAVE_QUIT; |
|
|
961 |
|
|
962 F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); |
|
|
963 } |
|
677
|
964 |
|
|
965 npts = nc; |
|
|
966 nsamples = nr; |
|
|
967 nn = 4*npts+15; |
|
1948
|
968 |
|
|
969 wsave.resize (nn); |
|
|
970 pwsave = wsave.fortran_vec (); |
|
|
971 |
|
|
972 Array<Complex> row (npts); |
|
|
973 Complex *prow = row.fortran_vec (); |
|
|
974 |
|
3887
|
975 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
976 |
|
1321
|
977 for (int j = 0; j < nsamples; j++) |
|
677
|
978 { |
|
4153
|
979 OCTAVE_QUIT; |
|
|
980 |
|
677
|
981 for (int i = 0; i < npts; i++) |
|
1948
|
982 prow[i] = tmp_data[i*nr + j]; |
|
|
983 |
|
3887
|
984 F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); |
|
677
|
985 |
|
1321
|
986 for (int i = 0; i < npts; i++) |
|
1948
|
987 tmp_data[i*nr + j] = prow[i]; |
|
677
|
988 } |
|
|
989 |
|
1948
|
990 return retval; |
|
677
|
991 } |
|
|
992 |
|
|
993 ComplexMatrix |
|
|
994 Matrix::ifourier2d (void) const |
|
|
995 { |
|
1948
|
996 ComplexMatrix retval; |
|
|
997 |
|
677
|
998 int nr = rows (); |
|
|
999 int nc = cols (); |
|
1948
|
1000 |
|
677
|
1001 int npts, nsamples; |
|
1948
|
1002 |
|
677
|
1003 if (nr == 1 || nc == 1) |
|
|
1004 { |
|
|
1005 npts = nr > nc ? nr : nc; |
|
|
1006 nsamples = 1; |
|
|
1007 } |
|
|
1008 else |
|
|
1009 { |
|
|
1010 npts = nr; |
|
|
1011 nsamples = nc; |
|
|
1012 } |
|
|
1013 |
|
|
1014 int nn = 4*npts+15; |
|
1948
|
1015 |
|
|
1016 Array<Complex> wsave (nn); |
|
|
1017 Complex *pwsave = wsave.fortran_vec (); |
|
|
1018 |
|
3585
|
1019 retval = ComplexMatrix (*this); |
|
1948
|
1020 Complex *tmp_data = retval.fortran_vec (); |
|
|
1021 |
|
3887
|
1022 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1023 |
|
|
1024 for (int j = 0; j < nsamples; j++) |
|
4153
|
1025 { |
|
|
1026 OCTAVE_QUIT; |
|
|
1027 |
|
|
1028 F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); |
|
|
1029 } |
|
677
|
1030 |
|
1321
|
1031 for (int j = 0; j < npts*nsamples; j++) |
|
3572
|
1032 tmp_data[j] = tmp_data[j] / static_cast<double> (npts); |
|
677
|
1033 |
|
|
1034 npts = nc; |
|
|
1035 nsamples = nr; |
|
|
1036 nn = 4*npts+15; |
|
1948
|
1037 |
|
|
1038 wsave.resize (nn); |
|
|
1039 pwsave = wsave.fortran_vec (); |
|
|
1040 |
|
|
1041 Array<Complex> row (npts); |
|
|
1042 Complex *prow = row.fortran_vec (); |
|
|
1043 |
|
3887
|
1044 F77_FUNC (cffti, CFFTI) (npts, pwsave); |
|
677
|
1045 |
|
1321
|
1046 for (int j = 0; j < nsamples; j++) |
|
677
|
1047 { |
|
4153
|
1048 OCTAVE_QUIT; |
|
|
1049 |
|
677
|
1050 for (int i = 0; i < npts; i++) |
|
1948
|
1051 prow[i] = tmp_data[i*nr + j]; |
|
|
1052 |
|
3887
|
1053 F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); |
|
677
|
1054 |
|
1321
|
1055 for (int i = 0; i < npts; i++) |
|
3572
|
1056 tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); |
|
677
|
1057 } |
|
|
1058 |
|
1948
|
1059 return retval; |
|
677
|
1060 } |
|
|
1061 |
|
3827
|
1062 #endif |
|
|
1063 |
|
458
|
1064 DET |
|
|
1065 Matrix::determinant (void) const |
|
|
1066 { |
|
|
1067 int info; |
|
|
1068 double rcond; |
|
4329
|
1069 return determinant (info, rcond, 0); |
|
458
|
1070 } |
|
|
1071 |
|
|
1072 DET |
|
|
1073 Matrix::determinant (int& info) const |
|
|
1074 { |
|
|
1075 double rcond; |
|
4329
|
1076 return determinant (info, rcond, 0); |
|
458
|
1077 } |
|
|
1078 |
|
|
1079 DET |
|
4329
|
1080 Matrix::determinant (int& info, double& rcond, int calc_cond) const |
|
458
|
1081 { |
|
|
1082 DET retval; |
|
|
1083 |
|
|
1084 int nr = rows (); |
|
|
1085 int nc = cols (); |
|
|
1086 |
|
|
1087 if (nr == 0 || nc == 0) |
|
|
1088 { |
|
|
1089 double d[2]; |
|
|
1090 d[0] = 1.0; |
|
|
1091 d[1] = 0.0; |
|
|
1092 retval = DET (d); |
|
|
1093 } |
|
|
1094 else |
|
|
1095 { |
|
1948
|
1096 Array<int> ipvt (nr); |
|
|
1097 int *pipvt = ipvt.fortran_vec (); |
|
|
1098 |
|
|
1099 Matrix atmp = *this; |
|
|
1100 double *tmp_data = atmp.fortran_vec (); |
|
|
1101 |
|
4329
|
1102 info = 0; |
|
|
1103 |
|
|
1104 /* Calculate the norm of the matrix, for later use */ |
|
|
1105 double anorm = 0; |
|
|
1106 if (calc_cond) |
|
|
1107 anorm = atmp.abs().sum().row(0).max(); |
|
|
1108 |
|
|
1109 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1110 |
|
|
1111 if (f77_exception_encountered) |
|
4329
|
1112 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
458
|
1113 else |
|
|
1114 { |
|
4329
|
1115 /* Throw-away extra info LAPACK gives so as to not change output */ |
|
|
1116 rcond = 0.; |
|
|
1117 if ( info != 0) |
|
1948
|
1118 { |
|
4329
|
1119 info = -1; |
|
|
1120 retval = DET (); |
|
|
1121 } |
|
|
1122 else |
|
1948
|
1123 { |
|
4329
|
1124 if (calc_cond) |
|
|
1125 { |
|
|
1126 /* Now calc the condition number for non-singular matrix */ |
|
|
1127 char job = '1'; |
|
|
1128 Array<double> z (4 * nc); |
|
|
1129 double *pz = z.fortran_vec (); |
|
|
1130 Array<int> iz (nc); |
|
|
1131 int *piz = iz.fortran_vec (); |
|
|
1132 |
|
|
1133 F77_XFCN (dgecon, DGECON, ( &job, nc, tmp_data, nr, anorm, |
|
|
1134 rcond, pz, piz, info)); |
|
|
1135 |
|
|
1136 if (f77_exception_encountered) |
|
|
1137 (*current_liboctave_error_handler) |
|
|
1138 ("unrecoverable error in dgecon"); |
|
|
1139 } |
|
|
1140 |
|
|
1141 if ( info != 0) |
|
|
1142 { |
|
|
1143 info = -1; |
|
|
1144 retval = DET (); |
|
|
1145 } |
|
|
1146 else |
|
|
1147 { |
|
|
1148 double d[2] = { 1., 0.}; |
|
|
1149 for (int i=0; i<nc; i++) |
|
|
1150 { |
|
|
1151 if (ipvt(i) != (i+1)) d[0] = -d[0]; |
|
|
1152 d[0] *= atmp(i,i); |
|
|
1153 if (d[0] == 0.) break; |
|
|
1154 while (fabs(d[0]) < 1.) |
|
|
1155 { |
|
|
1156 d[0] = 10. * d[0]; |
|
|
1157 d[1] = d[1] - 1.; |
|
|
1158 } |
|
|
1159 while (fabs(d[0]) >= 10.) |
|
|
1160 { |
|
|
1161 d[0] = 0.1 * d[0]; |
|
|
1162 d[1] = d[1] + 1.; |
|
|
1163 } |
|
|
1164 } |
|
|
1165 retval = DET (d); |
|
|
1166 } |
|
1948
|
1167 } |
|
458
|
1168 } |
|
|
1169 } |
|
|
1170 |
|
|
1171 return retval; |
|
|
1172 } |
|
|
1173 |
|
|
1174 Matrix |
|
|
1175 Matrix::solve (const Matrix& b) const |
|
|
1176 { |
|
|
1177 int info; |
|
|
1178 double rcond; |
|
4329
|
1179 return solve (b, info, rcond, 0); |
|
458
|
1180 } |
|
|
1181 |
|
|
1182 Matrix |
|
|
1183 Matrix::solve (const Matrix& b, int& info) const |
|
|
1184 { |
|
|
1185 double rcond; |
|
4329
|
1186 return solve (b, info, rcond, 0); |
|
458
|
1187 } |
|
|
1188 |
|
|
1189 Matrix |
|
532
|
1190 Matrix::solve (const Matrix& b, int& info, double& rcond) const |
|
458
|
1191 { |
|
3480
|
1192 return solve (b, info, rcond, 0); |
|
|
1193 } |
|
|
1194 |
|
|
1195 Matrix |
|
|
1196 Matrix::solve (const Matrix& b, int& info, double& rcond, |
|
|
1197 solve_singularity_handler sing_handler) const |
|
|
1198 { |
|
458
|
1199 Matrix retval; |
|
|
1200 |
|
|
1201 int nr = rows (); |
|
|
1202 int nc = cols (); |
|
1948
|
1203 |
|
458
|
1204 if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) |
|
1948
|
1205 (*current_liboctave_error_handler) |
|
|
1206 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1207 else |
|
|
1208 { |
|
1948
|
1209 info = 0; |
|
|
1210 |
|
|
1211 Array<int> ipvt (nr); |
|
|
1212 int *pipvt = ipvt.fortran_vec (); |
|
|
1213 |
|
|
1214 Matrix atmp = *this; |
|
|
1215 double *tmp_data = atmp.fortran_vec (); |
|
|
1216 |
|
4329
|
1217 Array<double> z (4 * nc); |
|
|
1218 double *pz = z.fortran_vec (); |
|
|
1219 Array<int> iz (nc); |
|
|
1220 int *piz = iz.fortran_vec (); |
|
|
1221 |
|
|
1222 /* Calculate the norm of the matrix, for later use */ |
|
|
1223 double anorm = atmp.abs().sum().row(0).max(); |
|
|
1224 |
|
|
1225 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1226 |
|
|
1227 if (f77_exception_encountered) |
|
4329
|
1228 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
1229 else |
|
|
1230 { |
|
4329
|
1231 /* Throw-away extra info LAPACK gives so as to not change output */ |
|
|
1232 rcond = 0.; |
|
|
1233 if ( info != 0) |
|
1948
|
1234 { |
|
|
1235 info = -2; |
|
3480
|
1236 |
|
|
1237 if (sing_handler) |
|
|
1238 sing_handler (rcond); |
|
|
1239 else |
|
|
1240 (*current_liboctave_error_handler) |
|
4329
|
1241 ("matrix singular to machine precision"); |
|
|
1242 |
|
|
1243 } |
|
|
1244 else |
|
1948
|
1245 { |
|
4329
|
1246 /* Now calculate the condition number for non-singular matrix */ |
|
|
1247 char job = '1'; |
|
|
1248 F77_XFCN (dgecon, DGECON, ( &job, nc, tmp_data, nr, anorm, |
|
|
1249 rcond, pz, piz, info)); |
|
|
1250 |
|
|
1251 if (f77_exception_encountered) |
|
|
1252 (*current_liboctave_error_handler) |
|
|
1253 ("unrecoverable error in dgecon"); |
|
|
1254 |
|
|
1255 if ( info != 0) |
|
|
1256 info = -2; |
|
|
1257 |
|
|
1258 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1259 |
|
|
1260 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
1948
|
1261 { |
|
4329
|
1262 info = -2; |
|
|
1263 |
|
|
1264 if (sing_handler) |
|
|
1265 sing_handler (rcond); |
|
|
1266 else |
|
|
1267 (*current_liboctave_error_handler) |
|
|
1268 ("matrix singular to machine precision, rcond = %g", |
|
|
1269 rcond); |
|
|
1270 } |
|
|
1271 else |
|
|
1272 { |
|
|
1273 retval = b; |
|
|
1274 double *result = retval.fortran_vec (); |
|
|
1275 |
|
|
1276 int b_nc = b.cols (); |
|
|
1277 |
|
|
1278 char job = 'N'; |
|
|
1279 F77_XFCN (dgetrs, DGETRS, (&job, nr, b_nc, tmp_data, nr, |
|
|
1280 pipvt, result, b.rows(), info)); |
|
|
1281 |
|
1948
|
1282 if (f77_exception_encountered) |
|
4329
|
1283 (*current_liboctave_error_handler) |
|
|
1284 ("unrecoverable error in dgetrs"); |
|
1948
|
1285 } |
|
|
1286 } |
|
|
1287 } |
|
458
|
1288 } |
|
|
1289 |
|
|
1290 return retval; |
|
|
1291 } |
|
|
1292 |
|
|
1293 ComplexMatrix |
|
|
1294 Matrix::solve (const ComplexMatrix& b) const |
|
|
1295 { |
|
|
1296 ComplexMatrix tmp (*this); |
|
|
1297 return tmp.solve (b); |
|
|
1298 } |
|
|
1299 |
|
|
1300 ComplexMatrix |
|
|
1301 Matrix::solve (const ComplexMatrix& b, int& info) const |
|
|
1302 { |
|
|
1303 ComplexMatrix tmp (*this); |
|
|
1304 return tmp.solve (b, info); |
|
|
1305 } |
|
|
1306 |
|
|
1307 ComplexMatrix |
|
|
1308 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const |
|
|
1309 { |
|
|
1310 ComplexMatrix tmp (*this); |
|
|
1311 return tmp.solve (b, info, rcond); |
|
|
1312 } |
|
|
1313 |
|
3480
|
1314 ComplexMatrix |
|
|
1315 Matrix::solve (const ComplexMatrix& b, int& info, double& rcond, |
|
|
1316 solve_singularity_handler sing_handler) const |
|
|
1317 { |
|
|
1318 ComplexMatrix tmp (*this); |
|
|
1319 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1320 } |
|
|
1321 |
|
458
|
1322 ColumnVector |
|
|
1323 Matrix::solve (const ColumnVector& b) const |
|
|
1324 { |
|
|
1325 int info; double rcond; |
|
|
1326 return solve (b, info, rcond); |
|
|
1327 } |
|
|
1328 |
|
|
1329 ColumnVector |
|
|
1330 Matrix::solve (const ColumnVector& b, int& info) const |
|
|
1331 { |
|
|
1332 double rcond; |
|
|
1333 return solve (b, info, rcond); |
|
|
1334 } |
|
|
1335 |
|
|
1336 ColumnVector |
|
532
|
1337 Matrix::solve (const ColumnVector& b, int& info, double& rcond) const |
|
458
|
1338 { |
|
3480
|
1339 return solve (b, info, rcond, 0); |
|
|
1340 } |
|
|
1341 |
|
|
1342 ColumnVector |
|
|
1343 Matrix::solve (const ColumnVector& b, int& info, double& rcond, |
|
|
1344 solve_singularity_handler sing_handler) const |
|
|
1345 { |
|
458
|
1346 ColumnVector retval; |
|
|
1347 |
|
|
1348 int nr = rows (); |
|
|
1349 int nc = cols (); |
|
1948
|
1350 |
|
458
|
1351 if (nr == 0 || nc == 0 || nr != nc || nr != b.length ()) |
|
1948
|
1352 (*current_liboctave_error_handler) |
|
|
1353 ("matrix dimension mismatch solution of linear equations"); |
|
458
|
1354 else |
|
|
1355 { |
|
1948
|
1356 info = 0; |
|
|
1357 |
|
|
1358 Array<int> ipvt (nr); |
|
|
1359 int *pipvt = ipvt.fortran_vec (); |
|
|
1360 |
|
|
1361 Matrix atmp = *this; |
|
|
1362 double *tmp_data = atmp.fortran_vec (); |
|
|
1363 |
|
4329
|
1364 Array<double> z (4 * nc); |
|
|
1365 double *pz = z.fortran_vec (); |
|
|
1366 Array<int> iz (nc); |
|
|
1367 int *piz = iz.fortran_vec (); |
|
|
1368 |
|
|
1369 /* Calculate the norm of the matrix, for later use */ |
|
|
1370 double anorm = atmp.abs().sum().row(0).max(); |
|
|
1371 |
|
|
1372 F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); |
|
1948
|
1373 |
|
|
1374 if (f77_exception_encountered) |
|
4329
|
1375 (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); |
|
1948
|
1376 else |
|
|
1377 { |
|
4329
|
1378 /* Throw-away extra info LAPACK gives so as to not change output */ |
|
|
1379 rcond = 0.; |
|
|
1380 if ( info > 0) |
|
1948
|
1381 { |
|
|
1382 info = -2; |
|
3480
|
1383 |
|
|
1384 if (sing_handler) |
|
|
1385 sing_handler (rcond); |
|
|
1386 else |
|
|
1387 (*current_liboctave_error_handler) |
|
4329
|
1388 ("matrix singular to machine precision"); |
|
|
1389 |
|
|
1390 } |
|
|
1391 else |
|
1948
|
1392 { |
|
4329
|
1393 /* Now calculate the condition number for non-singular matrix */ |
|
|
1394 char job = '1'; |
|
|
1395 F77_XFCN (dgecon, DGECON, ( &job, nc, tmp_data, nr, anorm, |
|
|
1396 rcond, pz, piz, info)); |
|
|
1397 |
|
1948
|
1398 if (f77_exception_encountered) |
|
4329
|
1399 (*current_liboctave_error_handler) |
|
|
1400 ("unrecoverable error in dgecon"); |
|
|
1401 |
|
|
1402 if ( info != 0) |
|
|
1403 info = -2; |
|
|
1404 |
|
|
1405 volatile double rcond_plus_one = rcond + 1.0; |
|
|
1406 |
|
|
1407 if (rcond_plus_one == 1.0 || xisnan (rcond)) |
|
|
1408 { |
|
|
1409 info = -2; |
|
|
1410 |
|
|
1411 if (sing_handler) |
|
|
1412 sing_handler (rcond); |
|
|
1413 else |
|
|
1414 (*current_liboctave_error_handler) |
|
|
1415 ("matrix singular to machine precision, rcond = %g", |
|
|
1416 rcond); |
|
|
1417 } |
|
|
1418 else |
|
|
1419 { |
|
|
1420 retval = b; |
|
|
1421 double *result = retval.fortran_vec (); |
|
|
1422 |
|
|
1423 char job = 'N'; |
|
|
1424 F77_XFCN (dgetrs, DGETRS, (&job, nr, 1, tmp_data, nr, pipvt, |
|
|
1425 result, b.length(), info)); |
|
|
1426 |
|
|
1427 if (f77_exception_encountered) |
|
|
1428 (*current_liboctave_error_handler) |
|
|
1429 ("unrecoverable error in dgetrs"); |
|
|
1430 } |
|
1948
|
1431 } |
|
|
1432 } |
|
458
|
1433 } |
|
4329
|
1434 |
|
458
|
1435 return retval; |
|
|
1436 } |
|
|
1437 |
|
|
1438 ComplexColumnVector |
|
|
1439 Matrix::solve (const ComplexColumnVector& b) const |
|
|
1440 { |
|
|
1441 ComplexMatrix tmp (*this); |
|
|
1442 return tmp.solve (b); |
|
|
1443 } |
|
|
1444 |
|
|
1445 ComplexColumnVector |
|
|
1446 Matrix::solve (const ComplexColumnVector& b, int& info) const |
|
|
1447 { |
|
|
1448 ComplexMatrix tmp (*this); |
|
|
1449 return tmp.solve (b, info); |
|
|
1450 } |
|
|
1451 |
|
|
1452 ComplexColumnVector |
|
|
1453 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const |
|
|
1454 { |
|
|
1455 ComplexMatrix tmp (*this); |
|
|
1456 return tmp.solve (b, info, rcond); |
|
|
1457 } |
|
|
1458 |
|
3480
|
1459 ComplexColumnVector |
|
|
1460 Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond, |
|
|
1461 solve_singularity_handler sing_handler) const |
|
|
1462 { |
|
|
1463 ComplexMatrix tmp (*this); |
|
|
1464 return tmp.solve (b, info, rcond, sing_handler); |
|
|
1465 } |
|
|
1466 |
|
458
|
1467 Matrix |
|
|
1468 Matrix::lssolve (const Matrix& b) const |
|
|
1469 { |
|
|
1470 int info; |
|
|
1471 int rank; |
|
|
1472 return lssolve (b, info, rank); |
|
|
1473 } |
|
|
1474 |
|
|
1475 Matrix |
|
|
1476 Matrix::lssolve (const Matrix& b, int& info) const |
|
|
1477 { |
|
|
1478 int rank; |
|
|
1479 return lssolve (b, info, rank); |
|
|
1480 } |
|
|
1481 |
|
|
1482 Matrix |
|
|
1483 Matrix::lssolve (const Matrix& b, int& info, int& rank) const |
|
|
1484 { |
|
1948
|
1485 Matrix retval; |
|
|
1486 |
|
458
|
1487 int nrhs = b.cols (); |
|
|
1488 |
|
|
1489 int m = rows (); |
|
|
1490 int n = cols (); |
|
|
1491 |
|
|
1492 if (m == 0 || n == 0 || m != b.rows ()) |
|
1948
|
1493 (*current_liboctave_error_handler) |
|
|
1494 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1495 else |
|
458
|
1496 { |
|
1948
|
1497 Matrix atmp = *this; |
|
|
1498 double *tmp_data = atmp.fortran_vec (); |
|
|
1499 |
|
|
1500 int nrr = m > n ? m : n; |
|
3754
|
1501 Matrix result (nrr, nrhs, 0.0); |
|
1948
|
1502 |
|
|
1503 for (int j = 0; j < nrhs; j++) |
|
|
1504 for (int i = 0; i < m; i++) |
|
|
1505 result.elem (i, j) = b.elem (i, j); |
|
|
1506 |
|
|
1507 double *presult = result.fortran_vec (); |
|
|
1508 |
|
|
1509 int len_s = m < n ? m : n; |
|
|
1510 Array<double> s (len_s); |
|
|
1511 double *ps = s.fortran_vec (); |
|
|
1512 |
|
|
1513 double rcond = -1.0; |
|
|
1514 |
|
3752
|
1515 // Ask DGELSS what the dimension of WORK should be. |
|
|
1516 |
|
|
1517 int lwork = -1; |
|
|
1518 |
|
|
1519 Array<double> work (1); |
|
1948
|
1520 |
|
|
1521 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
3752
|
1522 rcond, rank, work.fortran_vec (), |
|
|
1523 lwork, info)); |
|
1948
|
1524 |
|
|
1525 if (f77_exception_encountered) |
|
|
1526 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1527 else |
|
|
1528 { |
|
3752
|
1529 lwork = static_cast<int> (work(0)); |
|
|
1530 work.resize (lwork); |
|
|
1531 |
|
|
1532 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1533 nrr, ps, rcond, rank, |
|
|
1534 work.fortran_vec (), lwork, info)); |
|
|
1535 |
|
|
1536 if (f77_exception_encountered) |
|
|
1537 (*current_liboctave_error_handler) |
|
|
1538 ("unrecoverable error in dgelss"); |
|
|
1539 else |
|
|
1540 { |
|
|
1541 retval.resize (n, nrhs); |
|
|
1542 for (int j = 0; j < nrhs; j++) |
|
|
1543 for (int i = 0; i < n; i++) |
|
|
1544 retval.elem (i, j) = result.elem (i, j); |
|
|
1545 } |
|
1948
|
1546 } |
|
458
|
1547 } |
|
|
1548 |
|
|
1549 return retval; |
|
|
1550 } |
|
|
1551 |
|
|
1552 ComplexMatrix |
|
|
1553 Matrix::lssolve (const ComplexMatrix& b) const |
|
|
1554 { |
|
|
1555 ComplexMatrix tmp (*this); |
|
1484
|
1556 int info; |
|
|
1557 int rank; |
|
|
1558 return tmp.lssolve (b, info, rank); |
|
458
|
1559 } |
|
|
1560 |
|
|
1561 ComplexMatrix |
|
|
1562 Matrix::lssolve (const ComplexMatrix& b, int& info) const |
|
|
1563 { |
|
|
1564 ComplexMatrix tmp (*this); |
|
1484
|
1565 int rank; |
|
|
1566 return tmp.lssolve (b, info, rank); |
|
458
|
1567 } |
|
|
1568 |
|
|
1569 ComplexMatrix |
|
|
1570 Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const |
|
|
1571 { |
|
|
1572 ComplexMatrix tmp (*this); |
|
1484
|
1573 return tmp.lssolve (b, info, rank); |
|
458
|
1574 } |
|
|
1575 |
|
|
1576 ColumnVector |
|
|
1577 Matrix::lssolve (const ColumnVector& b) const |
|
|
1578 { |
|
|
1579 int info; |
|
1484
|
1580 int rank; |
|
|
1581 return lssolve (b, info, rank); |
|
458
|
1582 } |
|
|
1583 |
|
|
1584 ColumnVector |
|
|
1585 Matrix::lssolve (const ColumnVector& b, int& info) const |
|
|
1586 { |
|
|
1587 int rank; |
|
|
1588 return lssolve (b, info, rank); |
|
|
1589 } |
|
|
1590 |
|
|
1591 ColumnVector |
|
|
1592 Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const |
|
|
1593 { |
|
1948
|
1594 ColumnVector retval; |
|
|
1595 |
|
458
|
1596 int nrhs = 1; |
|
|
1597 |
|
|
1598 int m = rows (); |
|
|
1599 int n = cols (); |
|
|
1600 |
|
|
1601 if (m == 0 || n == 0 || m != b.length ()) |
|
1948
|
1602 (*current_liboctave_error_handler) |
|
|
1603 ("matrix dimension mismatch in solution of least squares problem"); |
|
|
1604 else |
|
458
|
1605 { |
|
1948
|
1606 Matrix atmp = *this; |
|
|
1607 double *tmp_data = atmp.fortran_vec (); |
|
|
1608 |
|
|
1609 int nrr = m > n ? m : n; |
|
|
1610 ColumnVector result (nrr); |
|
|
1611 |
|
|
1612 for (int i = 0; i < m; i++) |
|
|
1613 result.elem (i) = b.elem (i); |
|
|
1614 |
|
|
1615 double *presult = result.fortran_vec (); |
|
|
1616 |
|
|
1617 int len_s = m < n ? m : n; |
|
|
1618 Array<double> s (len_s); |
|
|
1619 double *ps = s.fortran_vec (); |
|
|
1620 |
|
|
1621 double rcond = -1.0; |
|
|
1622 |
|
3752
|
1623 // Ask DGELSS what the dimension of WORK should be. |
|
|
1624 |
|
|
1625 int lwork = -1; |
|
|
1626 |
|
|
1627 Array<double> work (1); |
|
|
1628 |
|
|
1629 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps, |
|
|
1630 rcond, rank, work.fortran_vec (), |
|
|
1631 lwork, info)); |
|
1948
|
1632 |
|
|
1633 if (f77_exception_encountered) |
|
|
1634 (*current_liboctave_error_handler) ("unrecoverable error in dgelss"); |
|
|
1635 else |
|
|
1636 { |
|
3752
|
1637 lwork = static_cast<int> (work(0)); |
|
|
1638 work.resize (lwork); |
|
|
1639 |
|
|
1640 F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, |
|
|
1641 nrr, ps, rcond, rank, |
|
|
1642 work.fortran_vec (), lwork, info)); |
|
|
1643 |
|
|
1644 if (f77_exception_encountered) |
|
|
1645 (*current_liboctave_error_handler) |
|
|
1646 ("unrecoverable error in dgelss"); |
|
|
1647 else |
|
|
1648 { |
|
|
1649 retval.resize (n); |
|
|
1650 for (int i = 0; i < n; i++) |
|
|
1651 retval.elem (i) = result.elem (i); |
|
|
1652 } |
|
1948
|
1653 } |
|
458
|
1654 } |
|
|
1655 |
|
|
1656 return retval; |
|
|
1657 } |
|
|
1658 |
|
|
1659 ComplexColumnVector |
|
|
1660 Matrix::lssolve (const ComplexColumnVector& b) const |
|
|
1661 { |
|
|
1662 ComplexMatrix tmp (*this); |
|
|
1663 return tmp.lssolve (b); |
|
|
1664 } |
|
|
1665 |
|
|
1666 ComplexColumnVector |
|
|
1667 Matrix::lssolve (const ComplexColumnVector& b, int& info) const |
|
|
1668 { |
|
|
1669 ComplexMatrix tmp (*this); |
|
|
1670 return tmp.lssolve (b, info); |
|
|
1671 } |
|
|
1672 |
|
|
1673 ComplexColumnVector |
|
|
1674 Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const |
|
|
1675 { |
|
|
1676 ComplexMatrix tmp (*this); |
|
|
1677 return tmp.lssolve (b, info, rank); |
|
|
1678 } |
|
|
1679 |
|
1819
|
1680 // Constants for matrix exponential calculation. |
|
|
1681 |
|
|
1682 static double padec [] = |
|
|
1683 { |
|
|
1684 5.0000000000000000e-1, |
|
|
1685 1.1666666666666667e-1, |
|
|
1686 1.6666666666666667e-2, |
|
|
1687 1.6025641025641026e-3, |
|
|
1688 1.0683760683760684e-4, |
|
|
1689 4.8562548562548563e-6, |
|
|
1690 1.3875013875013875e-7, |
|
|
1691 1.9270852604185938e-9, |
|
|
1692 }; |
|
|
1693 |
|
|
1694 Matrix |
|
|
1695 Matrix::expm (void) const |
|
|
1696 { |
|
|
1697 Matrix retval; |
|
|
1698 |
|
|
1699 Matrix m = *this; |
|
|
1700 |
|
|
1701 int nc = columns (); |
|
|
1702 |
|
3130
|
1703 // Preconditioning step 1: trace normalization to reduce dynamic |
|
|
1704 // range of poles, but avoid making stable eigenvalues unstable. |
|
|
1705 |
|
1819
|
1706 // trace shift value |
|
3331
|
1707 volatile double trshift = 0.0; |
|
1819
|
1708 |
|
|
1709 for (int i = 0; i < nc; i++) |
|
|
1710 trshift += m.elem (i, i); |
|
|
1711 |
|
|
1712 trshift /= nc; |
|
|
1713 |
|
3130
|
1714 if (trshift > 0.0) |
|
|
1715 { |
|
|
1716 for (int i = 0; i < nc; i++) |
|
|
1717 m.elem (i, i) -= trshift; |
|
|
1718 } |
|
1819
|
1719 |
|
3331
|
1720 // Preconditioning step 2: balancing; code follows development |
|
|
1721 // in AEPBAL |
|
|
1722 |
|
|
1723 double *p_m = m.fortran_vec (); |
|
|
1724 |
|
3468
|
1725 int info, ilo, ihi, ilos, ihis; |
|
|
1726 Array<double> dpermute (nc); |
|
|
1727 Array<double> dscale (nc); |
|
3466
|
1728 |
|
3468
|
1729 // permutation first |
|
|
1730 char job = 'P'; |
|
3469
|
1731 F77_XFCN (dgebal, DGEBAL, (&job, nc, p_m, nc, ilo, ihi, |
|
|
1732 dpermute.fortran_vec (), info, 1L, 1L)); |
|
3466
|
1733 |
|
3468
|
1734 // then scaling |
|
|
1735 job = 'S'; |
|
3469
|
1736 F77_XFCN (dgebal, DGEBAL, (&job, nc, p_m, nc, ilos, ihis, |
|
|
1737 dscale.fortran_vec (), info, 1L, 1L)); |
|
3331
|
1738 |
|
|
1739 if (f77_exception_encountered) |
|
|
1740 { |
|
|
1741 (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); |
|
|
1742 return retval; |
|
|
1743 } |
|
|
1744 |
|
1819
|
1745 // Preconditioning step 3: scaling. |
|
3331
|
1746 |
|
1819
|
1747 ColumnVector work(nc); |
|
3130
|
1748 double inf_norm; |
|
3331
|
1749 |
|
|
1750 F77_XFCN (xdlange, XDLANGE, ("I", nc, nc, m.fortran_vec (), nc, |
|
|
1751 work.fortran_vec (), inf_norm)); |
|
|
1752 |
|
|
1753 if (f77_exception_encountered) |
|
|
1754 { |
|
|
1755 (*current_liboctave_error_handler) ("unrecoverable error in dlange"); |
|
|
1756 return retval; |
|
|
1757 } |
|
1819
|
1758 |
|
|
1759 int sqpow = (int) (inf_norm > 0.0 |
|
|
1760 ? (1.0 + log (inf_norm) / log (2.0)) |
|
|
1761 : 0.0); |
|
3331
|
1762 |
|
1819
|
1763 // Check whether we need to square at all. |
|
3331
|
1764 |
|
1819
|
1765 if (sqpow < 0) |
|
|
1766 sqpow = 0; |
|
3331
|
1767 |
|
1819
|
1768 if (sqpow > 0) |
|
|
1769 { |
|
|
1770 double scale_factor = 1.0; |
|
|
1771 for (int i = 0; i < sqpow; i++) |
|
|
1772 scale_factor *= 2.0; |
|
3331
|
1773 |
|
1819
|
1774 m = m / scale_factor; |
|
|
1775 } |
|
3331
|
1776 |
|
1819
|
1777 // npp, dpp: pade' approx polynomial matrices. |
|
3331
|
1778 |
|
1819
|
1779 Matrix npp (nc, nc, 0.0); |
|
|
1780 Matrix dpp = npp; |
|
3331
|
1781 |
|
1819
|
1782 // Now powers a^8 ... a^1. |
|
3331
|
1783 |
|
1819
|
1784 int minus_one_j = -1; |
|
|
1785 for (int j = 7; j >= 0; j--) |
|
|
1786 { |
|
3573
|
1787 npp = m * npp + padec[j] * m; |
|
|
1788 dpp = m * dpp + (minus_one_j * padec[j]) * m; |
|
1819
|
1789 minus_one_j *= -1; |
|
|
1790 } |
|
3331
|
1791 |
|
1819
|
1792 // Zero power. |
|
3331
|
1793 |
|
1819
|
1794 dpp = -dpp; |
|
3130
|
1795 for (int j = 0; j < nc; j++) |
|
1819
|
1796 { |
|
|
1797 npp.elem (j, j) += 1.0; |
|
|
1798 dpp.elem (j, j) += 1.0; |
|
|
1799 } |
|
3331
|
1800 |
|
1819
|
1801 // Compute pade approximation = inverse (dpp) * npp. |
|
|
1802 |
|
3331
|
1803 retval = dpp.solve (npp, info); |
|
|
1804 |
|
1819
|
1805 // Reverse preconditioning step 3: repeated squaring. |
|
3331
|
1806 |
|
1819
|
1807 while (sqpow) |
|
|
1808 { |
|
|
1809 retval = retval * retval; |
|
|
1810 sqpow--; |
|
|
1811 } |
|
3331
|
1812 |
|
1819
|
1813 // Reverse preconditioning step 2: inverse balancing. |
|
3466
|
1814 // apply inverse scaling to computed exponential |
|
3468
|
1815 for (int i = 0; i < nc; i++) |
|
|
1816 for (int j = 0; j < nc; j++) |
|
|
1817 retval(i,j) *= dscale(i) / dscale(j); |
|
3466
|
1818 |
|
4153
|
1819 OCTAVE_QUIT; |
|
|
1820 |
|
3466
|
1821 // construct balancing permutation vector |
|
3468
|
1822 Array<int> ipermute (nc); |
|
|
1823 for (int i = 0; i < nc; i++) |
|
|
1824 ipermute(i) = i; // identity permutation |
|
3466
|
1825 |
|
|
1826 // leading permutations in forward order |
|
3468
|
1827 for (int i = 0; i < (ilo-1); i++) |
|
|
1828 { |
|
|
1829 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1830 int tmp = ipermute(i); |
|
|
1831 ipermute(i) = ipermute (swapidx); |
|
|
1832 ipermute(swapidx) = tmp; |
|
|
1833 } |
|
3466
|
1834 |
|
|
1835 // trailing permutations must be done in reverse order |
|
3468
|
1836 for (int i = nc - 1; i >= ihi; i--) |
|
|
1837 { |
|
|
1838 int swapidx = static_cast<int> (dpermute(i)) - 1; |
|
|
1839 int tmp = ipermute(i); |
|
|
1840 ipermute(i) = ipermute(swapidx); |
|
|
1841 ipermute(swapidx) = tmp; |
|
|
1842 } |
|
3466
|
1843 |
|
|
1844 // construct inverse balancing permutation vector |
|
3468
|
1845 Array<int> invpvec (nc); |
|
|
1846 for (int i = 0; i < nc; i++) |
|
|
1847 invpvec(ipermute(i)) = i; // Thanks to R. A. Lippert for this method |
|
4153
|
1848 |
|
|
1849 OCTAVE_QUIT; |
|
3466
|
1850 |
|
|
1851 Matrix tmpMat = retval; |
|
3468
|
1852 for (int i = 0; i < nc; i++) |
|
|
1853 for (int j = 0; j < nc; j++) |
|
|
1854 retval(i,j) = tmpMat(invpvec(i),invpvec(j)); |
|
3466
|
1855 |
|
1819
|
1856 // Reverse preconditioning step 1: fix trace normalization. |
|
3331
|
1857 |
|
3130
|
1858 if (trshift > 0.0) |
|
|
1859 retval = exp (trshift) * retval; |
|
|
1860 |
|
|
1861 return retval; |
|
1819
|
1862 } |
|
|
1863 |
|
458
|
1864 Matrix& |
|
|
1865 Matrix::operator += (const DiagMatrix& a) |
|
|
1866 { |
|
2385
|
1867 int nr = rows (); |
|
|
1868 int nc = cols (); |
|
|
1869 |
|
|
1870 int a_nr = a.rows (); |
|
|
1871 int a_nc = a.cols (); |
|
|
1872 |
|
|
1873 if (nr != a_nr || nc != a_nc) |
|
458
|
1874 { |
|
2385
|
1875 gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); |
|
458
|
1876 return *this; |
|
|
1877 } |
|
|
1878 |
|
|
1879 for (int i = 0; i < a.length (); i++) |
|
|
1880 elem (i, i) += a.elem (i, i); |
|
|
1881 |
|
|
1882 return *this; |
|
|
1883 } |
|
|
1884 |
|
|
1885 Matrix& |
|
|
1886 Matrix::operator -= (const DiagMatrix& a) |
|
|
1887 { |
|
2385
|
1888 int nr = rows (); |
|
|
1889 int nc = cols (); |
|
|
1890 |
|
|
1891 int a_nr = a.rows (); |
|
|
1892 int a_nc = a.cols (); |
|
|
1893 |
|
|
1894 if (nr != a_nr || nc != a_nc) |
|
458
|
1895 { |
|
2385
|
1896 gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); |
|
458
|
1897 return *this; |
|
|
1898 } |
|
|
1899 |
|
|
1900 for (int i = 0; i < a.length (); i++) |
|
|
1901 elem (i, i) -= a.elem (i, i); |
|
|
1902 |
|
|
1903 return *this; |
|
|
1904 } |
|
|
1905 |
|
|
1906 // unary operations |
|
|
1907 |
|
2964
|
1908 boolMatrix |
|
458
|
1909 Matrix::operator ! (void) const |
|
|
1910 { |
|
|
1911 int nr = rows (); |
|
|
1912 int nc = cols (); |
|
|
1913 |
|
2964
|
1914 boolMatrix b (nr, nc); |
|
458
|
1915 |
|
|
1916 for (int j = 0; j < nc; j++) |
|
|
1917 for (int i = 0; i < nr; i++) |
|
|
1918 b.elem (i, j) = ! elem (i, j); |
|
|
1919 |
|
|
1920 return b; |
|
|
1921 } |
|
|
1922 |
|
1205
|
1923 // column vector by row vector -> matrix operations |
|
458
|
1924 |
|
1205
|
1925 Matrix |
|
|
1926 operator * (const ColumnVector& v, const RowVector& a) |
|
458
|
1927 { |
|
1948
|
1928 Matrix retval; |
|
|
1929 |
|
1205
|
1930 int len = v.length (); |
|
3233
|
1931 |
|
|
1932 if (len != 0) |
|
1205
|
1933 { |
|
3233
|
1934 int a_len = a.length (); |
|
|
1935 |
|
|
1936 retval.resize (len, a_len); |
|
|
1937 double *c = retval.fortran_vec (); |
|
|
1938 |
|
|
1939 F77_XFCN (dgemm, DGEMM, ("N", "N", len, a_len, 1, 1.0, |
|
|
1940 v.data (), len, a.data (), 1, 0.0, |
|
|
1941 c, len, 1L, 1L)); |
|
|
1942 |
|
|
1943 if (f77_exception_encountered) |
|
|
1944 (*current_liboctave_error_handler) |
|
|
1945 ("unrecoverable error in dgemm"); |
|
1205
|
1946 } |
|
458
|
1947 |
|
1948
|
1948 return retval; |
|
458
|
1949 } |
|
|
1950 |
|
|
1951 // other operations. |
|
|
1952 |
|
|
1953 Matrix |
|
2676
|
1954 Matrix::map (d_d_Mapper f) const |
|
1205
|
1955 { |
|
2676
|
1956 Matrix b (*this); |
|
|
1957 return b.apply (f); |
|
1205
|
1958 } |
|
|
1959 |
|
3248
|
1960 boolMatrix |
|
|
1961 Matrix::map (b_d_Mapper f) const |
|
|
1962 { |
|
|
1963 int nr = rows (); |
|
|
1964 int nc = cols (); |
|
|
1965 |
|
|
1966 boolMatrix retval (nr, nc); |
|
|
1967 |
|
|
1968 for (int j = 0; j < nc; j++) |
|
|
1969 for (int i = 0; i < nr; i++) |
|
|
1970 retval(i,j) = f (elem(i,j)); |
|
|
1971 |
|
|
1972 return retval; |
|
|
1973 } |
|
|
1974 |
|
2676
|
1975 Matrix& |
|
|
1976 Matrix::apply (d_d_Mapper f) |
|
458
|
1977 { |
|
|
1978 double *d = fortran_vec (); // Ensures only one reference to my privates! |
|
|
1979 |
|
|
1980 for (int i = 0; i < length (); i++) |
|
|
1981 d[i] = f (d[i]); |
|
2676
|
1982 |
|
|
1983 return *this; |
|
458
|
1984 } |
|
|
1985 |
|
2385
|
1986 bool |
|
|
1987 Matrix::any_element_is_negative (void) const |
|
|
1988 { |
|
|
1989 int nr = rows (); |
|
|
1990 int nc = cols (); |
|
|
1991 |
|
|
1992 for (int j = 0; j < nc; j++) |
|
|
1993 for (int i = 0; i < nr; i++) |
|
|
1994 if (elem (i, j) < 0.0) |
|
|
1995 return true; |
|
|
1996 |
|
|
1997 return false; |
|
|
1998 } |
|
|
1999 |
|
|
2000 |
|
|
2001 bool |
|
|
2002 Matrix::any_element_is_inf_or_nan (void) const |
|
|
2003 { |
|
|
2004 int nr = rows (); |
|
|
2005 int nc = cols (); |
|
|
2006 |
|
|
2007 for (int j = 0; j < nc; j++) |
|
|
2008 for (int i = 0; i < nr; i++) |
|
|
2009 { |
|
|
2010 double val = elem (i, j); |
|
|
2011 if (xisinf (val) || xisnan (val)) |
|
|
2012 return 1; |
|
|
2013 } |
|
|
2014 return 0; |
|
|
2015 } |
|
|
2016 |
|
|
2017 bool |
|
|
2018 Matrix::all_elements_are_int_or_inf_or_nan (void) const |
|
|
2019 { |
|
|
2020 int nr = rows (); |
|
|
2021 int nc = cols (); |
|
|
2022 |
|
|
2023 for (int j = 0; j < nc; j++) |
|
|
2024 for (int i = 0; i < nr; i++) |
|
|
2025 { |
|
|
2026 double val = elem (i, j); |
|
|
2027 if (xisnan (val) || D_NINT (val) == val) |
|
|
2028 continue; |
|
|
2029 else |
|
|
2030 return false; |
|
|
2031 } |
|
|
2032 |
|
|
2033 return true; |
|
|
2034 } |
|
|
2035 |
|
1968
|
2036 // Return nonzero if any element of M is not an integer. Also extract |
|
|
2037 // the largest and smallest values and return them in MAX_VAL and MIN_VAL. |
|
|
2038 |
|
2385
|
2039 bool |
|
1968
|
2040 Matrix::all_integers (double& max_val, double& min_val) const |
|
|
2041 { |
|
|
2042 int nr = rows (); |
|
|
2043 int nc = cols (); |
|
|
2044 |
|
|
2045 if (nr > 0 && nc > 0) |
|
|
2046 { |
|
|
2047 max_val = elem (0, 0); |
|
|
2048 min_val = elem (0, 0); |
|
|
2049 } |
|
|
2050 else |
|
2385
|
2051 return false; |
|
1968
|
2052 |
|
|
2053 for (int j = 0; j < nc; j++) |
|
|
2054 for (int i = 0; i < nr; i++) |
|
|
2055 { |
|
|
2056 double val = elem (i, j); |
|
|
2057 |
|
|
2058 if (val > max_val) |
|
|
2059 max_val = val; |
|
|
2060 |
|
|
2061 if (val < min_val) |
|
|
2062 min_val = val; |
|
|
2063 |
|
|
2064 if (D_NINT (val) != val) |
|
2385
|
2065 return false; |
|
1968
|
2066 } |
|
2385
|
2067 |
|
|
2068 return true; |
|
1968
|
2069 } |
|
|
2070 |
|
2385
|
2071 bool |
|
1968
|
2072 Matrix::too_large_for_float (void) const |
|
|
2073 { |
|
|
2074 int nr = rows (); |
|
2385
|
2075 int nc = cols (); |
|
1968
|
2076 |
|
|
2077 for (int j = 0; j < nc; j++) |
|
|
2078 for (int i = 0; i < nr; i++) |
|
|
2079 { |
|
|
2080 double val = elem (i, j); |
|
|
2081 |
|
|
2082 if (val > FLT_MAX || val < FLT_MIN) |
|
2385
|
2083 return true; |
|
1968
|
2084 } |
|
|
2085 |
|
2385
|
2086 return false; |
|
1968
|
2087 } |
|
|
2088 |
|
4015
|
2089 // XXX FIXME XXX Do these really belong here? Maybe they should be |
|
|
2090 // in a base class? |
|
458
|
2091 |
|
2832
|
2092 boolMatrix |
|
4015
|
2093 Matrix::all (int dim) const |
|
458
|
2094 { |
|
4015
|
2095 MX_ALL_OP (dim); |
|
458
|
2096 } |
|
|
2097 |
|
2832
|
2098 boolMatrix |
|
4015
|
2099 Matrix::any (int dim) const |
|
458
|
2100 { |
|
4015
|
2101 MX_ANY_OP (dim); |
|
458
|
2102 } |
|
|
2103 |
|
|
2104 Matrix |
|
3723
|
2105 Matrix::cumprod (int dim) const |
|
458
|
2106 { |
|
4015
|
2107 MX_CUMULATIVE_OP (Matrix, double, *=); |
|
458
|
2108 } |
|
|
2109 |
|
|
2110 Matrix |
|
3723
|
2111 Matrix::cumsum (int dim) const |
|
458
|
2112 { |
|
4015
|
2113 MX_CUMULATIVE_OP (Matrix, double, +=); |
|
458
|
2114 } |
|
|
2115 |
|
|
2116 Matrix |
|
3723
|
2117 Matrix::prod (int dim) const |
|
458
|
2118 { |
|
3864
|
2119 MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); |
|
458
|
2120 } |
|
|
2121 |
|
|
2122 Matrix |
|
3723
|
2123 Matrix::sum (int dim) const |
|
458
|
2124 { |
|
3864
|
2125 MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); |
|
458
|
2126 } |
|
|
2127 |
|
|
2128 Matrix |
|
3723
|
2129 Matrix::sumsq (int dim) const |
|
458
|
2130 { |
|
3864
|
2131 #define ROW_EXPR \ |
|
|
2132 double d = elem (i, j); \ |
|
|
2133 retval.elem (i, 0) += d * d |
|
|
2134 |
|
|
2135 #define COL_EXPR \ |
|
|
2136 double d = elem (i, j); \ |
|
|
2137 retval.elem (0, j) += d * d |
|
|
2138 |
|
|
2139 MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); |
|
|
2140 |
|
|
2141 #undef ROW_EXPR |
|
|
2142 #undef COL_EXPR |
|
458
|
2143 } |
|
|
2144 |
|
2385
|
2145 Matrix |
|
|
2146 Matrix::abs (void) const |
|
|
2147 { |
|
|
2148 int nr = rows (); |
|
|
2149 int nc = cols (); |
|
|
2150 |
|
|
2151 Matrix retval (nr, nc); |
|
|
2152 |
|
|
2153 for (int j = 0; j < nc; j++) |
|
|
2154 for (int i = 0; i < nr; i++) |
|
|
2155 retval (i, j) = fabs (elem (i, j)); |
|
|
2156 |
|
|
2157 return retval; |
|
|
2158 } |
|
|
2159 |
|
458
|
2160 ColumnVector |
|
|
2161 Matrix::diag (void) const |
|
|
2162 { |
|
|
2163 return diag (0); |
|
|
2164 } |
|
|
2165 |
|
|
2166 ColumnVector |
|
|
2167 Matrix::diag (int k) const |
|
|
2168 { |
|
|
2169 int nnr = rows (); |
|
|
2170 int nnc = cols (); |
|
|
2171 if (k > 0) |
|
|
2172 nnc -= k; |
|
|
2173 else if (k < 0) |
|
|
2174 nnr += k; |
|
|
2175 |
|
|
2176 ColumnVector d; |
|
|
2177 |
|
|
2178 if (nnr > 0 && nnc > 0) |
|
|
2179 { |
|
|
2180 int ndiag = (nnr < nnc) ? nnr : nnc; |
|
|
2181 |
|
|
2182 d.resize (ndiag); |
|
|
2183 |
|
|
2184 if (k > 0) |
|
|
2185 { |
|
|
2186 for (int i = 0; i < ndiag; i++) |
|
|
2187 d.elem (i) = elem (i, i+k); |
|
|
2188 } |
|
|
2189 else if ( k < 0) |
|
|
2190 { |
|
|
2191 for (int i = 0; i < ndiag; i++) |
|
|
2192 d.elem (i) = elem (i-k, i); |
|
|
2193 } |
|
|
2194 else |
|
|
2195 { |
|
|
2196 for (int i = 0; i < ndiag; i++) |
|
|
2197 d.elem (i) = elem (i, i); |
|
|
2198 } |
|
|
2199 } |
|
|
2200 else |
|
3504
|
2201 std::cerr << "diag: requested diagonal out of range\n"; |
|
458
|
2202 |
|
|
2203 return d; |
|
|
2204 } |
|
|
2205 |
|
|
2206 ColumnVector |
|
|
2207 Matrix::row_min (void) const |
|
|
2208 { |
|
2354
|
2209 Array<int> index; |
|
|
2210 return row_min (index); |
|
458
|
2211 } |
|
|
2212 |
|
|
2213 ColumnVector |
|
2354
|
2214 Matrix::row_min (Array<int>& index) const |
|
458
|
2215 { |
|
|
2216 ColumnVector result; |
|
|
2217 |
|
|
2218 int nr = rows (); |
|
|
2219 int nc = cols (); |
|
|
2220 |
|
|
2221 if (nr > 0 && nc > 0) |
|
|
2222 { |
|
|
2223 result.resize (nr); |
|
2354
|
2224 index.resize (nr); |
|
458
|
2225 |
|
|
2226 for (int i = 0; i < nr; i++) |
|
|
2227 { |
|
3504
|
2228 int idx_j = 0; |
|
|
2229 |
|
|
2230 double tmp_min = elem (i, idx_j); |
|
2354
|
2231 |
|
|
2232 if (xisnan (tmp_min)) |
|
3504
|
2233 idx_j = -1; |
|
2354
|
2234 else |
|
|
2235 { |
|
|
2236 for (int j = 1; j < nc; j++) |
|
|
2237 { |
|
|
2238 double tmp = elem (i, j); |
|
|
2239 |
|
|
2240 if (xisnan (tmp)) |
|
|
2241 { |
|
3504
|
2242 idx_j = -1; |
|
2354
|
2243 break; |
|
|
2244 } |
|
|
2245 else if (tmp < tmp_min) |
|
|
2246 { |
|
3504
|
2247 idx_j = j; |
|
2354
|
2248 tmp_min = tmp; |
|
|
2249 } |
|
|
2250 } |
|
|
2251 } |
|
|
2252 |
|
3504
|
2253 result.elem (i) = (idx_j < 0) ? octave_NaN : tmp_min; |
|
|
2254 index.elem (i) = idx_j; |
|
458
|
2255 } |
|
|
2256 } |
|
|
2257 |
|
|
2258 return result; |
|
|
2259 } |
|
|
2260 |
|
|
2261 ColumnVector |
|
|
2262 Matrix::row_max (void) const |
|
|
2263 { |
|
2354
|
2264 Array<int> index; |
|
|
2265 return row_max (index); |
|
458
|
2266 } |
|
|
2267 |
|
|
2268 ColumnVector |
|
2354
|
2269 Matrix::row_max (Array<int>& index) const |
|
458
|
2270 { |
|
|
2271 ColumnVector result; |
|
|
2272 |
|
|
2273 int nr = rows (); |
|
|
2274 int nc = cols (); |
|
|
2275 |
|
|
2276 if (nr > 0 && nc > 0) |
|
|
2277 { |
|
|
2278 result.resize (nr); |
|
2354
|
2279 index.resize (nr); |
|
458
|
2280 |
|
|
2281 for (int i = 0; i < nr; i++) |
|
|
2282 { |
|
3504
|
2283 int idx_j = 0; |
|
|
2284 |
|
|
2285 double tmp_max = elem (i, idx_j); |
|
2354
|
2286 |
|
|
2287 if (xisnan (tmp_max)) |
|
3504
|
2288 idx_j = -1; |
|
2354
|
2289 else |
|
|
2290 { |
|
|
2291 for (int j = 1; j < nc; j++) |
|
|
2292 { |
|
|
2293 double tmp = elem (i, j); |
|
|
2294 |
|
|
2295 if (xisnan (tmp)) |
|
|
2296 { |
|
3504
|
2297 idx_j = -1; |
|
2354
|
2298 break; |
|
|
2299 } |
|
|
2300 else if (tmp > tmp_max) |
|
|
2301 { |
|
3504
|
2302 idx_j = j; |
|
2354
|
2303 tmp_max = tmp; |
|
|
2304 } |
|
|
2305 } |
|
|
2306 } |
|
|
2307 |
|
3504
|
2308 result.elem (i) = (idx_j < 0) ? octave_NaN : tmp_max; |
|
|
2309 index.elem (i) = idx_j; |
|
458
|
2310 } |
|
|
2311 } |
|
|
2312 |
|
|
2313 return result; |
|
|
2314 } |
|
|
2315 |
|
|
2316 RowVector |
|
|
2317 Matrix::column_min (void) const |
|
|
2318 { |
|
2354
|
2319 Array<int> index; |
|
|
2320 return column_min (index); |
|
458
|
2321 } |
|
2354
|
2322 |
|
458
|
2323 RowVector |
|
2354
|
2324 Matrix::column_min (Array<int>& index) const |
|
458
|
2325 { |
|
|
2326 RowVector result; |
|
|
2327 |
|
|
2328 int nr = rows (); |
|
|
2329 int nc = cols (); |
|
|
2330 |
|
|
2331 if (nr > 0 && nc > 0) |
|
|
2332 { |
|
|
2333 result.resize (nc); |
|
2354
|
2334 index.resize (nc); |
|
458
|
2335 |
|
|
2336 for (int j = 0; j < nc; j++) |
|
|
2337 { |
|
3504
|
2338 int idx_i = 0; |
|
|
2339 |
|
|
2340 double tmp_min = elem (idx_i, j); |
|
2354
|
2341 |
|
|
2342 if (xisnan (tmp_min)) |
|
3504
|
2343 idx_i = -1; |
|
2354
|
2344 else |
|
|
2345 { |
|
|
2346 for (int i = 1; i < nr; i++) |
|
|
2347 { |
|
|
2348 double tmp = elem (i, j); |
|
|
2349 |
|
|
2350 if (xisnan (tmp)) |
|
|
2351 { |
|
3504
|
2352 idx_i = -1; |
|
2354
|
2353 break; |
|
|
2354 } |
|
|
2355 else if (tmp < tmp_min) |
|
|
2356 { |
|
3504
|
2357 idx_i = i; |
|
2354
|
2358 tmp_min = tmp; |
|
|
2359 } |
|
|
2360 } |
|
|
2361 } |
|
|
2362 |
|
3504
|
2363 result.elem (j) = (idx_i < 0) ? octave_NaN : tmp_min; |
|
|
2364 index.elem (j) = idx_i; |
|
458
|
2365 } |
|
|
2366 } |
|
|
2367 |
|
|
2368 return result; |
|
|
2369 } |
|
|
2370 |
|
2354
|
2371 RowVector |
|
|
2372 Matrix::column_max (void) const |
|
|
2373 { |
|
|
2374 Array<int> index; |
|
|
2375 return column_max (index); |
|
|
2376 } |
|
458
|
2377 |
|
|
2378 RowVector |
|
2354
|
2379 Matrix::column_max (Array<int>& index) const |
|
458
|
2380 { |
|
|
2381 RowVector result; |
|
|
2382 |
|
|
2383 int nr = rows (); |
|
|
2384 int nc = cols (); |
|
|
2385 |
|
|
2386 if (nr > 0 && nc > 0) |
|
|
2387 { |
|
|
2388 result.resize (nc); |
|
2354
|
2389 index.resize (nc); |
|
458
|
2390 |
|
|
2391 for (int j = 0; j < nc; j++) |
|
|
2392 { |
|
3504
|
2393 int idx_i = 0; |
|
|
2394 |
|
|
2395 double tmp_max = elem (idx_i, j); |
|
2354
|
2396 |
|
|
2397 if (xisnan (tmp_max)) |
|
3504
|
2398 idx_i = -1; |
|
2354
|
2399 else |
|
|
2400 { |
|
|
2401 for (int i = 1; i < nr; i++) |
|
|
2402 { |
|
|
2403 double tmp = elem (i, j); |
|
|
2404 |
|
|
2405 if (xisnan (tmp)) |
|
|
2406 { |
|
3504
|
2407 idx_i = -1; |
|
2354
|
2408 break; |
|
|
2409 } |
|
|
2410 else if (tmp > tmp_max) |
|
|
2411 { |
|
3504
|
2412 idx_i = i; |
|
2354
|
2413 tmp_max = tmp; |
|
|
2414 } |
|
|
2415 } |
|
|
2416 } |
|
|
2417 |
|
3504
|
2418 result.elem (j) = (idx_i < 0) ? octave_NaN : tmp_max; |
|
|
2419 index.elem (j) = idx_i; |
|
458
|
2420 } |
|
|
2421 } |
|
|
2422 |
|
|
2423 return result; |
|
|
2424 } |
|
|
2425 |
|
3504
|
2426 std::ostream& |
|
|
2427 operator << (std::ostream& os, const Matrix& a) |
|
458
|
2428 { |
|
|
2429 for (int i = 0; i < a.rows (); i++) |
|
|
2430 { |
|
|
2431 for (int j = 0; j < a.cols (); j++) |
|
4130
|
2432 { |
|
|
2433 os << " "; |
|
|
2434 octave_write_double (os, a.elem (i, j)); |
|
|
2435 } |
|
458
|
2436 os << "\n"; |
|
|
2437 } |
|
|
2438 return os; |
|
|
2439 } |
|
|
2440 |
|
3504
|
2441 std::istream& |
|
|
2442 operator >> (std::istream& is, Matrix& a) |
|
458
|
2443 { |
|
|
2444 int nr = a.rows (); |
|
|
2445 int nc = a.cols (); |
|
|
2446 |
|
|
2447 if (nr < 1 || nc < 1) |
|
3504
|
2448 is.clear (std::ios::badbit); |
|
458
|
2449 else |
|
|
2450 { |
|
|
2451 double tmp; |
|
|
2452 for (int i = 0; i < nr; i++) |
|
|
2453 for (int j = 0; j < nc; j++) |
|
|
2454 { |
|
4130
|
2455 tmp = octave_read_double (is); |
|
458
|
2456 if (is) |
|
|
2457 a.elem (i, j) = tmp; |
|
|
2458 else |
|
2795
|
2459 goto done; |
|
458
|
2460 } |
|
|
2461 } |
|
|
2462 |
|
2795
|
2463 done: |
|
|
2464 |
|
458
|
2465 return is; |
|
|
2466 } |
|
|
2467 |
|
2317
|
2468 template <class T> |
|
3504
|
2469 void |
|
|
2470 read_int (std::istream& is, bool swap_bytes, T& val) |
|
2317
|
2471 { |
|
3145
|
2472 is.read (X_CAST (char *, &val), sizeof (T)); |
|
2317
|
2473 |
|
4282
|
2474 int t = sizeof (T); |
|
|
2475 |
|
|
2476 if (swap_bytes && t > 1) |
|
2317
|
2477 { |
|
4282
|
2478 switch (t) |
|
2317
|
2479 { |
|
|
2480 case 2: |
|
3145
|
2481 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2482 break; |
|
|
2483 |
|
|
2484 case 4: |
|
3145
|
2485 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2486 break; |
|
|
2487 |
|
|
2488 case 8: |
|
3145
|
2489 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2490 break; |
|
|
2491 |
|
|
2492 default: |
|
|
2493 (*current_liboctave_error_handler) |
|
|
2494 ("read_int: unrecognized data format!"); |
|
|
2495 } |
|
|
2496 } |
|
|
2497 } |
|
|
2498 |
|
3504
|
2499 template void read_int (std::istream&, bool, char&); |
|
|
2500 template void read_int (std::istream&, bool, signed char&); |
|
|
2501 template void read_int (std::istream&, bool, unsigned char&); |
|
|
2502 template void read_int (std::istream&, bool, short&); |
|
|
2503 template void read_int (std::istream&, bool, unsigned short&); |
|
|
2504 template void read_int (std::istream&, bool, int&); |
|
|
2505 template void read_int (std::istream&, bool, unsigned int&); |
|
|
2506 template void read_int (std::istream&, bool, long&); |
|
|
2507 template void read_int (std::istream&, bool, unsigned long&); |
|
2317
|
2508 |
|
|
2509 static inline bool |
|
3504
|
2510 do_read (std::istream& is, oct_data_conv::data_type dt, |
|
2317
|
2511 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2512 bool do_float_conversion, double& val) |
|
|
2513 { |
|
|
2514 bool retval = true; |
|
|
2515 |
|
|
2516 switch (dt) |
|
|
2517 { |
|
|
2518 case oct_data_conv::dt_char: |
|
|
2519 { |
|
|
2520 char tmp; |
|
|
2521 read_int (is, swap_bytes, tmp); |
|
|
2522 val = tmp; |
|
|
2523 } |
|
|
2524 break; |
|
|
2525 |
|
|
2526 case oct_data_conv::dt_schar: |
|
|
2527 { |
|
|
2528 signed char tmp; |
|
|
2529 read_int (is, swap_bytes, tmp); |
|
|
2530 val = tmp; |
|
|
2531 } |
|
|
2532 break; |
|
|
2533 |
|
|
2534 case oct_data_conv::dt_uchar: |
|
|
2535 { |
|
|
2536 unsigned char tmp; |
|
|
2537 read_int (is, swap_bytes, tmp); |
|
|
2538 val = tmp; |
|
|
2539 } |
|
|
2540 break; |
|
|
2541 |
|
|
2542 case oct_data_conv::dt_short: |
|
|
2543 { |
|
|
2544 short tmp; |
|
|
2545 read_int (is, swap_bytes, tmp); |
|
|
2546 val = tmp; |
|
|
2547 } |
|
|
2548 break; |
|
|
2549 |
|
|
2550 case oct_data_conv::dt_ushort: |
|
|
2551 { |
|
|
2552 unsigned short tmp; |
|
|
2553 read_int (is, swap_bytes, tmp); |
|
|
2554 val = tmp; |
|
|
2555 } |
|
|
2556 break; |
|
|
2557 |
|
|
2558 case oct_data_conv::dt_int: |
|
|
2559 { |
|
|
2560 int tmp; |
|
|
2561 read_int (is, swap_bytes, tmp); |
|
|
2562 val = tmp; |
|
|
2563 } |
|
|
2564 break; |
|
|
2565 |
|
|
2566 case oct_data_conv::dt_uint: |
|
|
2567 { |
|
|
2568 unsigned int tmp; |
|
|
2569 read_int (is, swap_bytes, tmp); |
|
|
2570 val = tmp; |
|
|
2571 } |
|
|
2572 break; |
|
|
2573 |
|
|
2574 case oct_data_conv::dt_long: |
|
|
2575 { |
|
|
2576 long tmp; |
|
|
2577 read_int (is, swap_bytes, tmp); |
|
|
2578 val = tmp; |
|
|
2579 } |
|
|
2580 break; |
|
|
2581 |
|
|
2582 case oct_data_conv::dt_ulong: |
|
|
2583 { |
|
|
2584 unsigned long tmp; |
|
|
2585 read_int (is, swap_bytes, tmp); |
|
|
2586 val = tmp; |
|
|
2587 } |
|
|
2588 break; |
|
|
2589 |
|
|
2590 case oct_data_conv::dt_float: |
|
|
2591 { |
|
|
2592 float f; |
|
|
2593 |
|
3145
|
2594 is.read (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2595 |
|
|
2596 if (do_float_conversion) |
|
|
2597 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2598 |
|
|
2599 val = f; |
|
|
2600 } |
|
|
2601 break; |
|
|
2602 |
|
|
2603 case oct_data_conv::dt_double: |
|
|
2604 { |
|
3145
|
2605 is.read (X_CAST (char *, &val), sizeof (double)); |
|
2317
|
2606 |
|
|
2607 if (do_float_conversion) |
|
|
2608 do_double_format_conversion (&val, 1, flt_fmt); |
|
|
2609 } |
|
|
2610 break; |
|
|
2611 |
|
|
2612 default: |
|
|
2613 retval = false; |
|
|
2614 (*current_liboctave_error_handler) |
|
|
2615 ("read: invalid type specification"); |
|
|
2616 break; |
|
|
2617 } |
|
|
2618 |
|
|
2619 return retval; |
|
|
2620 } |
|
1360
|
2621 |
|
458
|
2622 int |
|
3504
|
2623 Matrix::read (std::istream& is, int nr, int nc, |
|
2317
|
2624 oct_data_conv::data_type dt, int skip, |
|
|
2625 oct_mach_info::float_format flt_fmt) |
|
458
|
2626 { |
|
4293
|
2627 if (nr == 0 || nc == 0) |
|
|
2628 { |
|
|
2629 if (nr >= 0 && nc >= 0) |
|
|
2630 resize (nr, nc); |
|
|
2631 else |
|
|
2632 resize (0, 0); |
|
|
2633 |
|
|
2634 return 0; |
|
|
2635 } |
|
|
2636 |
|
2317
|
2637 int retval = -1; |
|
|
2638 |
|
|
2639 bool ok = true; |
|
|
2640 |
|
|
2641 int count = 0; |
|
|
2642 |
|
|
2643 double *data = 0; |
|
|
2644 int max_size = 0; |
|
|
2645 |
|
|
2646 int final_nr = 0; |
|
|
2647 int final_nc = 0; |
|
|
2648 |
|
|
2649 if (nr > 0) |
|
458
|
2650 { |
|
2317
|
2651 if (nc > 0) |
|
|
2652 { |
|
|
2653 resize (nr, nc, 0.0); |
|
|
2654 data = fortran_vec (); |
|
|
2655 max_size = nr * nc; |
|
|
2656 } |
|
|
2657 else |
|
|
2658 { |
|
|
2659 resize (nr, 32, 0.0); |
|
|
2660 data = fortran_vec (); |
|
|
2661 max_size = nr * 32; |
|
|
2662 } |
|
|
2663 } |
|
471
|
2664 else |
|
|
2665 { |
|
2317
|
2666 resize (32, 1, 0.0); |
|
|
2667 data = fortran_vec (); |
|
|
2668 max_size = 32; |
|
|
2669 } |
|
|
2670 |
|
|
2671 oct_mach_info::float_format native_flt_fmt |
|
|
2672 = oct_mach_info::float_format (); |
|
|
2673 |
|
|
2674 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2675 |
|
|
2676 // XXX FIXME XXX -- byte order for Cray? |
|
|
2677 |
|
|
2678 bool swap_bytes = false; |
|
|
2679 |
|
|
2680 if (oct_mach_info::words_big_endian ()) |
|
|
2681 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2682 || flt_fmt == oct_mach_info::vax_g |
|
|
2683 || flt_fmt == oct_mach_info::vax_g); |
|
|
2684 else |
|
|
2685 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2686 |
|
|
2687 for (;;) |
|
|
2688 { |
|
|
2689 // XXX FIXME XXX -- maybe there should be a special case for |
|
|
2690 // skip == 0. |
|
|
2691 |
|
|
2692 if (is) |
|
|
2693 { |
|
|
2694 if (nr > 0 && nc > 0 && count == max_size) |
|
|
2695 { |
|
|
2696 final_nr = nr; |
|
|
2697 final_nc = nc; |
|
|
2698 |
|
|
2699 break; |
|
|
2700 } |
|
|
2701 |
|
4083
|
2702 double tmp = 0.0; |
|
|
2703 |
|
|
2704 ok = do_read (is, dt, flt_fmt, swap_bytes, do_float_conversion, tmp); |
|
|
2705 |
|
|
2706 if (ok) |
|
2317
|
2707 { |
|
4083
|
2708 if (is) |
|
2317
|
2709 { |
|
4083
|
2710 if (count == max_size) |
|
2317
|
2711 { |
|
4083
|
2712 max_size *= 2; |
|
|
2713 |
|
|
2714 if (nr > 0) |
|
|
2715 resize (nr, max_size / nr, 0.0); |
|
|
2716 else |
|
|
2717 resize (max_size, 1, 0.0); |
|
|
2718 |
|
|
2719 data = fortran_vec (); |
|
2317
|
2720 } |
|
3180
|
2721 |
|
4083
|
2722 data[count++] = tmp; |
|
|
2723 } |
|
|
2724 |
|
|
2725 if (skip != 0) |
|
|
2726 is.seekg (skip, std::ios::cur); |
|
|
2727 |
|
|
2728 if (is.eof ()) |
|
|
2729 { |
|
|
2730 if (nr > 0) |
|
2317
|
2731 { |
|
4083
|
2732 if (count > nr) |
|
2317
|
2733 { |
|
4083
|
2734 final_nr = nr; |
|
|
2735 final_nc = (count - 1) / nr + 1; |
|
|
2736 } |
|
|
2737 else |
|
|
2738 { |
|
|
2739 final_nr = count; |
|
|
2740 final_nc = 1; |
|
2317
|
2741 } |
|
|
2742 } |
|
4083
|
2743 else |
|
|
2744 { |
|
|
2745 final_nr = count; |
|
|
2746 final_nc = 1; |
|
|
2747 } |
|
|
2748 |
|
|
2749 break; |
|
2317
|
2750 } |
|
|
2751 } |
|
|
2752 else |
|
|
2753 { |
|
|
2754 ok = false; |
|
|
2755 break; |
|
|
2756 } |
|
|
2757 } |
|
|
2758 else |
|
|
2759 { |
|
|
2760 ok = false; |
|
|
2761 break; |
|
|
2762 } |
|
|
2763 } |
|
|
2764 |
|
|
2765 if (ok) |
|
|
2766 { |
|
|
2767 resize (final_nr, final_nc, 0.0); |
|
|
2768 |
|
|
2769 retval = count; |
|
458
|
2770 } |
|
|
2771 |
|
2317
|
2772 return retval; |
|
|
2773 } |
|
|
2774 |
|
|
2775 template <class T> |
|
3504
|
2776 void |
|
|
2777 write_int (std::ostream& os, bool swap_bytes, T val) |
|
2317
|
2778 { |
|
4282
|
2779 int t = sizeof (T); |
|
|
2780 |
|
|
2781 if (swap_bytes && t > 1) |
|
2317
|
2782 { |
|
4282
|
2783 switch (t) |
|
2317
|
2784 { |
|
|
2785 case 2: |
|
3145
|
2786 swap_2_bytes (X_CAST (char *, &val)); |
|
2317
|
2787 break; |
|
|
2788 |
|
|
2789 case 4: |
|
3145
|
2790 swap_4_bytes (X_CAST (char *, &val)); |
|
2317
|
2791 break; |
|
|
2792 |
|
|
2793 case 8: |
|
3145
|
2794 swap_8_bytes (X_CAST (char *, &val)); |
|
2317
|
2795 break; |
|
|
2796 |
|
|
2797 default: |
|
|
2798 (*current_liboctave_error_handler) |
|
|
2799 ("write_int: unrecognized data format!"); |
|
|
2800 } |
|
|
2801 } |
|
|
2802 |
|
3145
|
2803 os.write (X_CAST (char *, &val), sizeof (T)); |
|
458
|
2804 } |
|
|
2805 |
|
3504
|
2806 template void write_int (std::ostream&, bool, char); |
|
|
2807 template void write_int (std::ostream&, bool, signed char); |
|
|
2808 template void write_int (std::ostream&, bool, unsigned char); |
|
|
2809 template void write_int (std::ostream&, bool, short); |
|
|
2810 template void write_int (std::ostream&, bool, unsigned short); |
|
|
2811 template void write_int (std::ostream&, bool, int); |
|
|
2812 template void write_int (std::ostream&, bool, unsigned int); |
|
|
2813 template void write_int (std::ostream&, bool, long); |
|
|
2814 template void write_int (std::ostream&, bool, unsigned long); |
|
2317
|
2815 |
|
|
2816 static inline bool |
|
3504
|
2817 do_write (std::ostream& os, double d, oct_data_conv::data_type dt, |
|
2317
|
2818 oct_mach_info::float_format flt_fmt, bool swap_bytes, |
|
|
2819 bool do_float_conversion) |
|
|
2820 { |
|
|
2821 bool retval = true; |
|
|
2822 |
|
|
2823 switch (dt) |
|
|
2824 { |
|
|
2825 case oct_data_conv::dt_char: |
|
3145
|
2826 write_int (os, swap_bytes, X_CAST (char, d)); |
|
2317
|
2827 break; |
|
|
2828 |
|
|
2829 case oct_data_conv::dt_schar: |
|
3145
|
2830 write_int (os, swap_bytes, X_CAST (signed char, d)); |
|
2317
|
2831 break; |
|
|
2832 |
|
|
2833 case oct_data_conv::dt_uchar: |
|
3145
|
2834 write_int (os, swap_bytes, X_CAST (unsigned char, d)); |
|
2317
|
2835 break; |
|
|
2836 |
|
|
2837 case oct_data_conv::dt_short: |
|
3145
|
2838 write_int (os, swap_bytes, X_CAST (short, d)); |
|
2317
|
2839 break; |
|
|
2840 |
|
|
2841 case oct_data_conv::dt_ushort: |
|
3145
|
2842 write_int (os, swap_bytes, X_CAST (unsigned short, d)); |
|
2317
|
2843 break; |
|
|
2844 |
|
|
2845 case oct_data_conv::dt_int: |
|
3145
|
2846 write_int (os, swap_bytes, X_CAST (int, d)); |
|
2317
|
2847 break; |
|
|
2848 |
|
|
2849 case oct_data_conv::dt_uint: |
|
3145
|
2850 write_int (os, swap_bytes, X_CAST (unsigned int, d)); |
|
2317
|
2851 break; |
|
|
2852 |
|
|
2853 case oct_data_conv::dt_long: |
|
3145
|
2854 write_int (os, swap_bytes, X_CAST (long, d)); |
|
2317
|
2855 break; |
|
|
2856 |
|
|
2857 case oct_data_conv::dt_ulong: |
|
3145
|
2858 write_int (os, swap_bytes, X_CAST (unsigned long, d)); |
|
2317
|
2859 break; |
|
|
2860 |
|
|
2861 case oct_data_conv::dt_float: |
|
|
2862 { |
|
2800
|
2863 float f = d; |
|
2317
|
2864 |
|
|
2865 if (do_float_conversion) |
|
|
2866 do_float_format_conversion (&f, 1, flt_fmt); |
|
|
2867 |
|
3145
|
2868 os.write (X_CAST (char *, &f), sizeof (float)); |
|
2317
|
2869 } |
|
|
2870 break; |
|
|
2871 |
|
|
2872 case oct_data_conv::dt_double: |
|
|
2873 { |
|
|
2874 if (do_float_conversion) |
|
|
2875 do_double_format_conversion (&d, 1, flt_fmt); |
|
|
2876 |
|
3145
|
2877 os.write (X_CAST (char *, &d), sizeof (double)); |
|
2317
|
2878 } |
|
|
2879 break; |
|
|
2880 |
|
|
2881 default: |
|
|
2882 retval = false; |
|
|
2883 (*current_liboctave_error_handler) |
|
|
2884 ("write: invalid type specification"); |
|
|
2885 break; |
|
|
2886 } |
|
|
2887 |
|
|
2888 return retval; |
|
|
2889 } |
|
1360
|
2890 |
|
458
|
2891 int |
|
3504
|
2892 Matrix::write (std::ostream& os, oct_data_conv::data_type dt, int skip, |
|
2317
|
2893 oct_mach_info::float_format flt_fmt) |
|
458
|
2894 { |
|
2317
|
2895 int retval = -1; |
|
|
2896 |
|
|
2897 bool ok = true; |
|
|
2898 |
|
|
2899 int count = 0; |
|
|
2900 |
|
|
2901 const double *d = data (); |
|
|
2902 |
|
|
2903 int n = length (); |
|
|
2904 |
|
|
2905 oct_mach_info::float_format native_flt_fmt |
|
|
2906 = oct_mach_info::float_format (); |
|
|
2907 |
|
|
2908 bool do_float_conversion = (flt_fmt != native_flt_fmt); |
|
|
2909 |
|
|
2910 // XXX FIXME XXX -- byte order for Cray? |
|
|
2911 |
|
|
2912 bool swap_bytes = false; |
|
|
2913 |
|
|
2914 if (oct_mach_info::words_big_endian ()) |
|
|
2915 swap_bytes = (flt_fmt == oct_mach_info::ieee_little_endian |
|
|
2916 || flt_fmt == oct_mach_info::vax_g |
|
|
2917 || flt_fmt == oct_mach_info::vax_g); |
|
|
2918 else |
|
|
2919 swap_bytes = (flt_fmt == oct_mach_info::ieee_big_endian); |
|
|
2920 |
|
|
2921 for (int i = 0; i < n; i++) |
|
458
|
2922 { |
|
2317
|
2923 if (os) |
|
|
2924 { |
|
|
2925 if (skip != 0) |
|
3504
|
2926 os.seekp (skip, std::ios::cur); |
|
2317
|
2927 |
|
|
2928 if (os) |
|
|
2929 { |
|
|
2930 ok = do_write (os, d[i], dt, flt_fmt, swap_bytes, |
|
|
2931 do_float_conversion); |
|
|
2932 |
|
|
2933 if (os && ok) |
|
|
2934 count++; |
|
|
2935 else |
|
|
2936 break; |
|
|
2937 } |
|
|
2938 else |
|
|
2939 { |
|
|
2940 ok = false; |
|
|
2941 break; |
|
|
2942 } |
|
|
2943 } |
|
|
2944 else |
|
|
2945 { |
|
|
2946 ok = false; |
|
|
2947 break; |
|
|
2948 } |
|
471
|
2949 } |
|
458
|
2950 |
|
2317
|
2951 if (ok) |
|
|
2952 retval = count; |
|
|
2953 |
|
|
2954 return retval; |
|
458
|
2955 } |
|
|
2956 |
|
2317
|
2957 |
|
|
2958 |
|
1819
|
2959 Matrix |
|
|
2960 Givens (double x, double y) |
|
|
2961 { |
|
|
2962 double cc, s, temp_r; |
|
|
2963 |
|
3887
|
2964 F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); |
|
1819
|
2965 |
|
|
2966 Matrix g (2, 2); |
|
|
2967 |
|
|
2968 g.elem (0, 0) = cc; |
|
|
2969 g.elem (1, 1) = cc; |
|
|
2970 g.elem (0, 1) = s; |
|
|
2971 g.elem (1, 0) = -s; |
|
|
2972 |
|
|
2973 return g; |
|
|
2974 } |
|
|
2975 |
|
|
2976 Matrix |
|
|
2977 Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) |
|
|
2978 { |
|
|
2979 Matrix retval; |
|
|
2980 |
|
|
2981 // XXX FIXME XXX -- need to check that a, b, and c are all the same |
|
|
2982 // size. |
|
|
2983 |
|
|
2984 // Compute Schur decompositions. |
|
|
2985 |
|
|
2986 SCHUR as (a, "U"); |
|
|
2987 SCHUR bs (b, "U"); |
|
|
2988 |
|
|
2989 // Transform c to new coordinates. |
|
|
2990 |
|
|
2991 Matrix ua = as.unitary_matrix (); |
|
|
2992 Matrix sch_a = as.schur_matrix (); |
|
|
2993 |
|
|
2994 Matrix ub = bs.unitary_matrix (); |
|
|
2995 Matrix sch_b = bs.schur_matrix (); |
|
|
2996 |
|
|
2997 Matrix cx = ua.transpose () * c * ub; |
|
|
2998 |
|
|
2999 // Solve the sylvester equation, back-transform, and return the |
|
|
3000 // solution. |
|
|
3001 |
|
|
3002 int a_nr = a.rows (); |
|
|
3003 int b_nr = b.rows (); |
|
|
3004 |
|
|
3005 double scale; |
|
|
3006 int info; |
|
|
3007 |
|
1950
|
3008 double *pa = sch_a.fortran_vec (); |
|
|
3009 double *pb = sch_b.fortran_vec (); |
|
|
3010 double *px = cx.fortran_vec (); |
|
|
3011 |
|
|
3012 F77_XFCN (dtrsyl, DTRSYL, ("N", "N", 1, a_nr, b_nr, pa, a_nr, pb, |
|
|
3013 b_nr, px, a_nr, scale, info, 1L, 1L)); |
|
|
3014 |
|
|
3015 |
|
|
3016 if (f77_exception_encountered) |
|
|
3017 (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); |
|
|
3018 else |
|
|
3019 { |
|
|
3020 // XXX FIXME XXX -- check info? |
|
1819
|
3021 |
|
1950
|
3022 retval = -ua*cx*ub.transpose (); |
|
|
3023 } |
|
1819
|
3024 |
|
|
3025 return retval; |
|
|
3026 } |
|
|
3027 |
|
2828
|
3028 // matrix by matrix -> matrix operations |
|
|
3029 |
|
|
3030 Matrix |
|
|
3031 operator * (const Matrix& m, const Matrix& a) |
|
|
3032 { |
|
|
3033 Matrix retval; |
|
|
3034 |
|
|
3035 int nr = m.rows (); |
|
|
3036 int nc = m.cols (); |
|
|
3037 |
|
|
3038 int a_nr = a.rows (); |
|
|
3039 int a_nc = a.cols (); |
|
|
3040 |
|
|
3041 if (nc != a_nr) |
|
|
3042 gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); |
|
|
3043 else |
|
|
3044 { |
|
|
3045 if (nr == 0 || nc == 0 || a_nc == 0) |
|
|
3046 retval.resize (nr, a_nc, 0.0); |
|
|
3047 else |
|
|
3048 { |
|
|
3049 int ld = nr; |
|
|
3050 int lda = a_nr; |
|
|
3051 |
|
|
3052 retval.resize (nr, a_nc); |
|
|
3053 double *c = retval.fortran_vec (); |
|
|
3054 |
|
|
3055 F77_XFCN (dgemm, DGEMM, ("N", "N", nr, a_nc, nc, 1.0, |
|
|
3056 m.data (), ld, a.data (), lda, 0.0, |
|
|
3057 c, nr, 1L, 1L)); |
|
|
3058 |
|
|
3059 if (f77_exception_encountered) |
|
|
3060 (*current_liboctave_error_handler) |
|
|
3061 ("unrecoverable error in dgemm"); |
|
|
3062 } |
|
|
3063 } |
|
|
3064 |
|
|
3065 return retval; |
|
|
3066 } |
|
|
3067 |
|
4309
|
3068 // XXX FIXME XXX -- it would be nice to share code among the min/max |
|
|
3069 // functions below. |
|
|
3070 |
|
|
3071 #define EMPTY_RETURN_CHECK(T) \ |
|
|
3072 if (nr == 0 || nc == 0) \ |
|
|
3073 return T (nr, nc); |
|
|
3074 |
|
|
3075 Matrix |
|
|
3076 min (double d, const Matrix& m) |
|
|
3077 { |
|
|
3078 int nr = m.rows (); |
|
|
3079 int nc = m.columns (); |
|
|
3080 |
|
|
3081 EMPTY_RETURN_CHECK (Matrix); |
|
|
3082 |
|
|
3083 Matrix result (nr, nc); |
|
|
3084 |
|
|
3085 for (int j = 0; j < nc; j++) |
|
|
3086 for (int i = 0; i < nr; i++) |
|
|
3087 { |
|
|
3088 OCTAVE_QUIT; |
|
|
3089 result (i, j) = xmin (d, m (i, j)); |
|
|
3090 } |
|
|
3091 |
|
|
3092 return result; |
|
|
3093 } |
|
|
3094 |
|
|
3095 Matrix |
|
|
3096 min (const Matrix& m, double d) |
|
|
3097 { |
|
|
3098 int nr = m.rows (); |
|
|
3099 int nc = m.columns (); |
|
|
3100 |
|
|
3101 EMPTY_RETURN_CHECK (Matrix); |
|
|
3102 |
|
|
3103 Matrix result (nr, nc); |
|
|
3104 |
|
|
3105 for (int j = 0; j < nc; j++) |
|
|
3106 for (int i = 0; i < nr; i++) |
|
|
3107 { |
|
|
3108 OCTAVE_QUIT; |
|
|
3109 result (i, j) = xmin (m (i, j), d); |
|
|
3110 } |
|
|
3111 |
|
|
3112 return result; |
|
|
3113 } |
|
|
3114 |
|
|
3115 Matrix |
|
|
3116 min (const Matrix& a, const Matrix& b) |
|
|
3117 { |
|
|
3118 int nr = a.rows (); |
|
|
3119 int nc = a.columns (); |
|
|
3120 |
|
|
3121 if (nr != b.rows () || nc != b.columns ()) |
|
|
3122 { |
|
|
3123 (*current_liboctave_error_handler) |
|
|
3124 ("two-arg min expecting args of same size"); |
|
|
3125 return Matrix (); |
|
|
3126 } |
|
|
3127 |
|
|
3128 EMPTY_RETURN_CHECK (Matrix); |
|
|
3129 |
|
|
3130 Matrix result (nr, nc); |
|
|
3131 |
|
|
3132 for (int j = 0; j < nc; j++) |
|
|
3133 for (int i = 0; i < nr; i++) |
|
|
3134 { |
|
|
3135 OCTAVE_QUIT; |
|
|
3136 result (i, j) = xmin (a (i, j), b (i, j)); |
|
|
3137 } |
|
|
3138 |
|
|
3139 return result; |
|
|
3140 } |
|
|
3141 |
|
|
3142 Matrix |
|
|
3143 max (double d, const Matrix& m) |
|
|
3144 { |
|
|
3145 int nr = m.rows (); |
|
|
3146 int nc = m.columns (); |
|
|
3147 |
|
|
3148 EMPTY_RETURN_CHECK (Matrix); |
|
|
3149 |
|
|
3150 Matrix result (nr, nc); |
|
|
3151 |
|
|
3152 for (int j = 0; j < nc; j++) |
|
|
3153 for (int i = 0; i < nr; i++) |
|
|
3154 { |
|
|
3155 OCTAVE_QUIT; |
|
|
3156 result (i, j) = xmax (d, m (i, j)); |
|
|
3157 } |
|
|
3158 |
|
|
3159 return result; |
|
|
3160 } |
|
|
3161 |
|
|
3162 Matrix |
|
|
3163 max (const Matrix& m, double d) |
|
|
3164 { |
|
|
3165 int nr = m.rows (); |
|
|
3166 int nc = m.columns (); |
|
|
3167 |
|
|
3168 EMPTY_RETURN_CHECK (Matrix); |
|
|
3169 |
|
|
3170 Matrix result (nr, nc); |
|
|
3171 |
|
|
3172 for (int j = 0; j < nc; j++) |
|
|
3173 for (int i = 0; i < nr; i++) |
|
|
3174 { |
|
|
3175 OCTAVE_QUIT; |
|
|
3176 result (i, j) = xmax (m (i, j), d); |
|
|
3177 } |
|
|
3178 |
|
|
3179 return result; |
|
|
3180 } |
|
|
3181 |
|
|
3182 Matrix |
|
|
3183 max (const Matrix& a, const Matrix& b) |
|
|
3184 { |
|
|
3185 int nr = a.rows (); |
|
|
3186 int nc = a.columns (); |
|
|
3187 |
|
|
3188 if (nr != b.rows () || nc != b.columns ()) |
|
|
3189 { |
|
|
3190 (*current_liboctave_error_handler) |
|
|
3191 ("two-arg max expecting args of same size"); |
|
|
3192 return Matrix (); |
|
|
3193 } |
|
|
3194 |
|
|
3195 EMPTY_RETURN_CHECK (Matrix); |
|
|
3196 |
|
|
3197 Matrix result (nr, nc); |
|
|
3198 |
|
|
3199 for (int j = 0; j < nc; j++) |
|
|
3200 for (int i = 0; i < nr; i++) |
|
|
3201 { |
|
|
3202 OCTAVE_QUIT; |
|
|
3203 result (i, j) = xmax (a (i, j), b (i, j)); |
|
|
3204 } |
|
|
3205 |
|
|
3206 return result; |
|
|
3207 } |
|
|
3208 |
|
2870
|
3209 MS_CMP_OPS(Matrix, , double, ) |
|
3504
|
3210 MS_BOOL_OPS(Matrix, double, 0.0) |
|
2870
|
3211 |
|
|
3212 SM_CMP_OPS(double, , Matrix, ) |
|
3504
|
3213 SM_BOOL_OPS(double, Matrix, 0.0) |
|
2870
|
3214 |
|
|
3215 MM_CMP_OPS(Matrix, , Matrix, ) |
|
3504
|
3216 MM_BOOL_OPS(Matrix, Matrix, 0.0) |
|
2870
|
3217 |
|
458
|
3218 /* |
|
|
3219 ;;; Local Variables: *** |
|
|
3220 ;;; mode: C++ *** |
|
|
3221 ;;; End: *** |
|
|
3222 */ |
